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  • Introduction

General observations

formal logic

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Alfred North Whitehead

formal logic , the abstract study of propositions , statements, or assertively used sentences and of deductive arguments. The discipline abstracts from the content of these elements the structures or logical forms that they embody. The logician customarily uses a symbolic notation to express such structures clearly and unambiguously and to enable manipulations and tests of validity to be more easily applied. Although the following discussion freely employs the technical notation of modern symbolic logic, its symbols are introduced gradually and with accompanying explanations so that the serious and attentive general reader should be able to follow the development of ideas.

Formal logic is an a priori , and not an empirical , study. In this respect it contrasts with the natural sciences and with all other disciplines that depend on observation for their data. Its nearest analogy is to pure mathematics ; indeed, many logicians and pure mathematicians would regard their respective subjects as indistinguishable, or as merely two stages of the same unified discipline. Formal logic, therefore, is not to be confused with the empirical study of the processes of reasoning , which belongs to psychology . It must also be distinguished from the art of correct reasoning, which is the practical skill of applying logical principles to particular cases; and, even more sharply, it must be distinguished from the art of persuasion, in which invalid arguments are sometimes more effective than valid ones.

Probably the most natural approach to formal logic is through the idea of the validity of an argument of the kind known as deductive. A deductive argument can be roughly characterized as one in which the claim is made that some proposition (the conclusion ) follows with strict necessity from some other proposition or propositions (the premises )—i.e., that it would be inconsistent or self-contradictory to assert the premises but deny the conclusion.

If a deductive argument is to succeed in establishing the truth of its conclusion, two quite distinct conditions must be met: first, the conclusion must really follow from the premises—i.e., the deduction of the conclusion from the premises must be logically correct—and, second, the premises themselves must be true. An argument meeting both these conditions is called sound. Of these two conditions, the logician as such is concerned only with the first; the second, the determination of the truth or falsity of the premises, is the task of some special discipline or of common observation appropriate to the subject matter of the argument. When the conclusion of an argument is correctly deducible from its premises, the inference from the premises to the conclusion is said to be (deductively) valid, irrespective of whether the premises are true or false. Other ways of expressing the fact that an inference is deductively valid are to say that the truth of the premises gives (or would give) an absolute guarantee of the truth of the conclusion or that it would involve a logical inconsistency (as distinct from a mere mistake of fact) to suppose that the premises were true but the conclusion false.

The deductive inferences with which formal logic is concerned are, as the name suggests, those for which validity depends not on any features of their subject matter but on their form or structure. Thus, the two inferences (1) Every dog is a mammal. Some quadrupeds are dogs. ∴ Some quadrupeds are mammals. and (2) Every anarchist is a believer in free love. Some members of the government party are anarchists. ∴ Some members of the government party are believers in free love. differ in subject matter and hence require different procedures to check the truth or falsity of their premises. But their validity is ensured by what they have in common—namely, that the argument in each is of the form (3) Every X is a Y . Some Z ’s are X ’s. ∴ Some Z ’s are Y ’s.

Line (3) above may be called an inference form , and (1) and (2) are then instances of that inference form. The letters— X , Y , and Z —in (3) mark the places into which expressions of a certain type may be inserted. Symbols used for this purpose are known as variables ; their use is analogous to that of the x in algebra , which marks the place into which a numeral can be inserted. An instance of an inference form is produced by replacing all the variables in it by appropriate expressions (i.e., ones that make sense in the context) and by doing so uniformly (i.e., by substituting the same expression wherever the same variable recurs). The feature of (3) that guarantees that every instance of it will be valid is its construction in such a manner that every uniform way of replacing its variables to make the premises true automatically makes the conclusion true also, or, in other words, that no instance of it can have true premises but a false conclusion. In virtue of this feature, the form (3) is termed a valid inference form. In contrast, (4) Every X is a Y . Some Z ’s are Y ’s. ∴ Some Z ’s are X ’s. is not a valid inference form, for, although instances of it can be produced in which premises and conclusion are all true, instances of it can also be produced in which the premises are true but the conclusion is false—e.g., (5) Every dog is a mammal. Some winged creatures are mammals. ∴ Some winged creatures are dogs.

Formal logic as a study is concerned with inference forms rather than with particular instances of them. One of its tasks is to discriminate between valid and invalid inference forms and to explore and systematize the relations that hold among valid ones.

Closely related to the idea of a valid inference form is that of a valid proposition form. A proposition form is an expression of which the instances (produced as before by appropriate and uniform replacements for variables) are not inferences from several propositions to a conclusion but rather propositions taken individually, and a valid proposition form is one for which all of the instances are true propositions. A simple example is (6) Nothing is both an X and a non- X . Formal logic is concerned with proposition forms as well as with inference forms. The study of proposition forms can, in fact, be made to include that of inference forms in the following way: let the premises of any given inference form (taken together) be abbreviated by alpha (α) and its conclusion by beta (β). Then the condition stated above for the validity of the inference form “α, therefore β” amounts to saying that no instance of the proposition form “α and not-β” is true—i.e., that every instance of the proposition form (7) Not both: α and not-β is true—or that line (7), fully spelled out, of course, is a valid proposition form. The study of proposition forms, however, cannot be similarly accommodated under the study of inference forms, and so for reasons of comprehensiveness it is usual to regard formal logic as the study of proposition forms. Because a logician’s handling of proposition forms is in many ways analogous to a mathematician’s handling of numerical formulas, the systems he constructs are often called calculi.

Much of the work of a logician proceeds at a more abstract level than that of the foregoing discussion. Even a formula such as (3) above, though not referring to any specific subject matter, contains expressions like “every” and “is a,” which are thought of as having a definite meaning, and the variables are intended to mark the places for expressions of one particular kind (roughly, common nouns or class names). It is possible, however—and for some purposes it is essential—to study formulas without attaching even this degree of meaningfulness to them. The construction of a system of logic , in fact, involves two distinguishable processes: one consists in setting up a symbolic apparatus—a set of symbols, rules for stringing these together into formulas, and rules for manipulating these formulas; the second consists in attaching certain meanings to these symbols and formulas. If only the former is done, the system is said to be uninterpreted , or purely formal; if the latter is done as well, the system is said to be interpreted. This distinction is important, because systems of logic turn out to have certain properties quite independently of any interpretations that may be placed upon them. An axiomatic system of logic can be taken as an example—i.e., a system in which certain unproved formulas, known as axioms , are taken as starting points, and further formulas ( theorems ) are proved on the strength of these. As will appear later ( see below Axiomatization of PC ), the question whether a sequence of formulas in an axiomatic system is a proof or not depends solely on which formulas are taken as axioms and on what the rules are for deriving theorems from axioms, and not at all on what the theorems or axioms mean. Moreover, a given uninterpreted system is in general capable of being interpreted equally well in a number of different ways; hence, in studying an uninterpreted system, one is studying the structure that is common to a variety of interpreted systems. Normally a logician who constructs a purely formal system does have a particular interpretation in mind, and his motive for constructing it is the belief that when this interpretation is given to it, the formulas of the system will be able to express true principles in some field of thought; but, for the above reasons among others, he will usually take care to describe the formulas and state the rules of the system without reference to interpretation and to indicate as a separate matter the interpretation that he has in mind.

Many of the ideas used in the exposition of formal logic , including some that are mentioned above, raise problems that belong to philosophy rather than to logic itself. Examples are: What is the correct analysis of the notion of truth ? What is a proposition, and how is it related to the sentence by which it is expressed? Are there some kinds of sound reasoning that are neither deductive nor inductive ? Fortunately, it is possible to learn to do formal logic without having satisfactory answers to such questions, just as it is possible to do mathematics without answering questions belonging to the philosophy of mathematics such as: Are numbers real objects or mental constructs?

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Mathematics LibreTexts

2.1: Statements and Logical Operators

PREVIEW ACTIVITY \(\PageIndex{1}\): Compound Statements

Mathematicians often develop ways to construct new mathematical objects from existing mathematical objects. It is possible to form new statements from existing statements by connecting the statements with words such as “and” and “or” or by negating the statement. A logical operator (or connective ) on mathematical statements is a word or combination of words that combines one or more mathematical statements to make a new mathematical statement. A compound statement is a statement that contains one or more operators. Because some operators are used so frequently in logic and mathematics, we give them names and use special symbols to represent them.

Some comments about the disjunction. It is important to understand the use of the operator “or.” In mathematics, we use the “ inclusive or ” unless stated otherwise. This means that \(P \vee Q\) is true when both \(P\) and \(Q\) are true and also when only one of them is true. That is, \(P \vee Q\) is true when at least one of \(P\) or \(Q\) is true, or \(P \vee Q\) is false only when both \(P\) and \(Q\) are false.

A different use of the word “or” is the “ exclusive or .” For the exclusive or, the resulting statement is false when both statements are true. That is, “\(P\) exclusive or \(Q\)” is true only when exactly one of \(P\) or \(Q\) is true. In everyday life, we often use the exclusive or. When someone says, “At the intersection, turn left or go straight,” this person is using the exclusive or.

Some comments about the negation . Although the statement, \(\urcorner P\), can be read as “It is not the case that \(P\),” there are often betters ways to say or write this in English. For example, we would usually say (or write):

\(P\): 15 is odd \(Q\): 15 is prime write each of the following statements as English sentences and determine

whether they are true or false. (a) \(P \wedge Q\). (b) \(P \vee Q\). (c) \(P \wedge \urcorner Q\). (d) \(\urcorner P \vee \urcorner Q\).

P : 15 is odd R: 15 < 17

write each of the following statements in symbolic form using the operators\(\wedge\), \(\vee\), and \(\urcorner\)

(a) 15 \(\ge\) 17. (b) 15 is odd or 15 \(\ge\) 17. (c) 15 is even or 15 <17. (d) 15 is odd and 15 \(\ge\) 17.

PREVIEW ACTIVITY\(\PageIndex{2}\): Truth Values of Statements

We will use the following two statements for all of this Preview Activity:

In each of the following four parts, a truth value will be assigned to statements \(P\) and \(Q\). For example, in Question (1), we will assume that each statement is true. In Question (2), we will assume that \(P\) is true and \(Q\) is false. In each part, determine the truth value of each of the following statements:

(a) (\(P \wedge Q\)) It is raining and Daisy is playing golf.

(b) (\(P \vee Q\)) It is raining or Daisy is playing golf.

(c) (\(P \to Q\)) If it is raining, then Daisy is playing golf.

(d) (\(\urcorner P\)) It is not raining.

Which of the four statements [(a) through (d)] are true and which are false in each of the following four situations?

1. When \(P\) is true (it is raining) and \(Q\) is true (Daisy is playing golf). 2. When \(P\) is true (it is raining) and \(Q\) is false (Daisy is not playing golf). 3. When \(P\) is false (it is not raining) and \(Q\) is true (Daisy is playing golf). 4. When \(P\) is false (it is not raining) and \(Q\) is false (Daisy is not playing golf).

In the preview activities for this section, we learned about compound statements and their truth values. This information can be summarized with truth tables as is shown below.

Rather than memorizing the truth tables, for many people it is easier to remember the rules summarized in Table 2.1.

Other Forms of Conditional Statements

Conditional statements are extremely important in mathematics because almost all mathematical theorems are (or can be) stated in the form of a conditional statement in the following form:

If “certain conditions are met,” then “something happens.”

It is imperative that all students studying mathematics thoroughly understand the meaning of a conditional statement and the truth table for a conditional statement.


In all of these cases, \(P\) is the hypothesis of the conditional statement and \(Q\) is the conclusion of the conditional statement.

Progress Check 2.1: The "Only if" statemenT

Recall that a quadrilateral is a four-sided polygon. Let \(S\) represent the following true conditional statement:

If a quadrilateral is a square, then it is a rectangle.

Write this conditional statement in English using

Add texts here. Do not delete this text first.

Constructing Truth Tables

Truth tables for compound statements can be constructed by using the truth tables for the basic connectives. To illustrate this, we will construct a truth table for. \((P \wedge \urcorner Q) \to R\). The first step is to determine the number of rows needed.

The next step is to determine the columns to be used. One way to do this is to work backward from the form of the given statement. For \((P \wedge \urcorner Q) \to R\), the last step is to deal with the conditional operator \((\to)\). To do this, we need to know the truth values of \((P \wedge \urcorner Q)\) and \(R\). To determine the truth values for \((P \wedge \urcorner Q)\), we need to apply the rules for the conjunction operator \((\wedge)\) and we need to know the truth values for \(P\) and \(\urcorner Q\).

Table 2.2 is a completed truth table for \((P \wedge \urcorner Q) \to R\) with the step numbers indicated at the bottom of each column. The step numbers correspond to the order in which the columns were completed.

The last column entered is the truth table for the statement \((P \wedge \urcorner Q) \to R\) using the set up in the first three columns.

Progress Check 2.2: Constructing Truth Tables

Construct a truth table for each of the following statements:

Do any of these statements have the same truth table?

The Biconditional Statement

Some mathematical results are stated in the form “\(P\) if and only if \(Q\)” or “\(P\) is necessary and sufficient for \(Q\).” An example would be, “A triangle is equilateral if and only if its three interior angles are congruent.” The symbolic form for the biconditional statement “\(P\) if and only if \(Q\)” is \(P \leftrightarrow Q\). In order to determine a truth table for a biconditional statement, it is instructive to look carefully at the form of the phrase “\(P\) if and only if \(Q\).” The word “and” suggests that this statement is a conjunction. Actually it is a conjunction of the statements “\(P\) if \(Q\)” and “\(P\) only if \(Q\).” The symbolic form of this conjunction is \([(Q \to P) \wedge (P \to Q]\).

Progress Check 2.3: The Truth Table for the Biconditional Statement

Complete a truth table for \([(Q \to P) \wedge (P \to Q]\). Use the following columns: \(P\), \(Q\), \(Q \to P\), \(P \to Q\), and \([(Q \to P) \wedge (P \to Q]\). The last column of this table will be the truth for \(P \leftrightarrow Q\).

Other Forms of the Biconditional Statement

As with the conditional statement, there are some common ways to express the biconditional statement, \(P \leftrightarrow Q\), in the English language.

Tautologies and Contradictions

Definition: tautology

A tautology is a compound statement S that is true for all possible combinations of truth values of the component statements that are part of \(S\). A contradiction is a compound statement that is false for all possible combinations of truth values of the component statements that are part of \(S\).

That is, a tautology is necessarily true in all circumstances, and a contradiction is necessarily false in all circumstances.

Progress Check 2.4 (Tautologies and Contradictions)

For statements \(P\) and \(Q\):

Exercises for Section 2.1

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Examples of Logic: 4 Main Types of Reasoning

Example of Formal Logic

In simple words, logic is “the study of correct reasoning, especially regarding making inferences.” Logic began as a philosophical term and is now used in other disciplines like math and computer science. While the definition sounds simple enough, understanding logic is a little more complex. Use logic examples to help you learn to use logic properly.

Definitions of Logic

Logic can include the act of reasoning by humans in order to form thoughts and opinions, as well as classifications and judgments. Some forms of logic can also be performed by computers and even animals.

Logic can be defined as :

“The study of truths based completely on the meanings of the terms they contain.”

Logic is a process for making a conclusion and a tool you can use.

Definition of Logic in Philosophy

Logic is a branch of philosophy. There are different schools of thought on logic in philosophy, but the typical version is called classical elementary logic or classical first-order logic . In this discipline, philosophers try to distinguish good reasoning from bad reasoning.

Definition of Logic in Mathematics

Logic is also an area of mathematics. Mathematical logic uses propositional variables , which are often letters, to represent propositions .

Types of Logic With Examples

Generally speaking, there are four types of logic.

Informal Logic

Informal logic is what’s typically used in daily reasoning. This is the reasoning and arguments you make in your personal exchanges with others.

Premises: Nikki saw a black cat on her way to work. At work, Nikki got fired.

Conclusion: Black cats are bad luck.

Explanation: This is a big generalization and can’t be verified.

Premises: There is no evidence that penicillin is bad for you. I use penicillin without any problems.

Conclusion: Penicillin is safe for everyone.

Explanation: The personal experience here or lack of knowledge isn’t verifiable.

Premises: My mom is a celebrity. I live with my mom.

Conclusion: I am a celebrity.

Explanation: There is more to proving fame that assuming it will rub off.

Formal Logic

In formal logic , you use deductive reasoning and the premises must be true. You follow the premises to reach a formal conclusion.

Premises: Every person who lives in Quebec lives in Canada. Everyone in Canada lives in North America.

Conclusion: Every person who lives in Quebec lives in North America.

Explanation: Only true facts are presented here.

Premises: All spiders have eight legs. Black Widows are a type of spider.

Conclusion: Black Widows have eight legs.

Explanation: This argument isn’t controversial.

Premises: Bicycles have two wheels. Jan is riding a bicycle.

Conclusion: Jan is riding on two wheels.

Explanation: The premises are true and so is the conclusion.

Symbolic Logic

Symbolic logic deals with how symbols relate to each other. It assigns symbols to verbal reasoning in order to be able to check the veracity of the statements through a mathematical process. You typically see this type of logic used in calculus.

Symbolic logic example:

Mathematical Logic

In mathematical logic, you apply formal logic to math. This type of logic is part of the basis for the logic used in computer sciences. Mathematical logic and symbolic logic are often used interchangeably.

Types of Reasoning With Examples

Each type of logic could include deductive reasoning, inductive reasoning, or both.

Deductive Reasoning Examples

Deductive reasoning provides complete evidence of the truth of its conclusion. It uses a specific and accurate premise that leads to a specific and accurate conclusion. With correct premises, the conclusion to this type of argument is verifiable and correct.

Premises: All squares are rectangles. All rectangles have four sides.

Conclusion: All squares have four sides.

Premises: All people are mortal. You are a person.

Conclusion: You are mortal.

Premises: All trees have trunks. An oak tree is a tree.

Conclusion: The oak tree has a trunk.

Inductive Logic Examples

Inductive reasoning is "bottom up," meaning that it takes specific information and makes a broad generalization that is considered probable, allowing for the fact that the conclusion may not be accurate. This type of reasoning usually involves a rule being established based on a series of repeated experiences.

Premises: An umbrella prevents you from getting wet in the rain. Ashley took her umbrella, and she did not get wet.

Conclusion: In this case, you could use inductive reasoning to offer an opinion that it was probably raining.

Explanation: Your conclusion, however, would not necessarily be accurate because Ashley would have remained dry whether it rained and she had an umbrella, or it didn't rain at all.

Premises: Every three-year-old you see at the park each afternoon spends most of their time crying and screaming.

Conclusion: All three-year-olds must spend their afternoon screaming.

Explanation: This would not necessarily be correct, because you haven’t seen every three-year-old in the world during the afternoon to verify it.

Premises: Twelve out of the 20 houses on the block burned down. Each fire was caused by faulty wiring.

Conclusion: If more than half the homes have faulty wiring, all homes on the block have faulty wiring.

Explanation: You do not know this conclusion to be verifiably true, but it is probable.

Premises: Red lights prevent accidents. Mike did not have an accident while driving today.

Conclusion: Mike must have stopped at a red light.

Explanation: Mike might not have encountered any traffic signals at all. Therefore, he might have been able to avoid accidents even without stopping at a red light.

Follow the Logic

As these examples show, you can use logic to solve problems and to draw conclusions. Sometimes those conclusions are correct conclusions, and sometimes they are inaccurate. When you use deductive reasoning, you arrive at correct logical arguments while inductive reasoning may or may not provide you with a correct outcome. Check out examples of logical fallacies to see what incorrect logical reasoning looks like.

Statement in Logic

what is statement logic

The word Logic is derived from the Greek word ‘Logos’ which means reason. Logic deals with the methods of reasoning. Logic is a process by which we arrive at a conclusion from known statements or assertions with the help of valid assumptions. The valid assumptions are known as laws of logic. The Greek philosopher and thinker Aristotle laid the foundation of the study of logic in the systematic form. Logic associated with mathematics is called mathematical logic. The mathematical approach to logic is developed by English philosopher and mathematician George Boole. Hence logic is also referred as Boolean Logic or Symbolic Logic.


Logic helps in the development of systematic and logical reasoning skills. It helps in understanding the precise meaning of statements of theorems, the converse of theorems, and corollaries of the theorem. It is the basis of circuit designing, artificial intelligence, and computer programming.

Statement in Logic:

Language is the medium of communication of thoughts. We do so by using sentences simple or complex. They may be assertive or imperative or exclamatory or interrogative or suggestive or wishes. A declarative sentence, which is either true or false, but not both simultaneously, is called a statement in logic.

Sentences which are incomplete or imperative or interrogative or exclamatory or suggestive or wishes or perceptions are not taken as statements in logic. An open sentence is a sentence whose truth value can vary according to some conditions which are not stated in the sentence. e.g. It is white in colour.

In logic, the statements are denoted by small case letters particularly p, q, r, ….

Law of the Excluded Middle:

A statement is either true or false. It can not be both true and false and also neither true nor false. This fact is known as the law of the excluded middle.

Truth Value of a Statement:

To find the Truth Value of a Statement:

Determine which of the following sentences are statements in logic. If not give a reason . If a statement, then find its truth value.

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Unit 1: Lesson 11

A quick guide to conditional logic

A quick guide to translating common prose statements into conditional logic statements, if x, then y, x only if y, only x are y, any x is/are y, every x is y, no x is/are y, x cannot be y, without x there can be no y, x requires y, in order for x to be true, y must be true, x depends on y, x happens whenever y happens, no x unless y.

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Conditional Statement

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In the study of logic, there are two types of statements, conditional statement and bi-conditional statement . These statements are formed by combining two statements, which are called compound statements . Suppose a statement is- if it rains, then we don’t play. This is a combination of two statements. These types of statements are mainly used in computer programming languages such as c, c++, etc. Let us learn more here with examples.

Conditional Statement Definition

A conditional statement is represented in the form of “if…then”. Let p and q are the two statements, then statements p and q can be written as per different conditions, such as;

Points to remember:

Truth Table for Conditional Statement

The truth table for any two inputs, say A and B is given by;

Example: We have a conditional statement If it is raining, we will not play. Let, A: It is raining and B: we will not play. Then;

What is a Bi-Conditional Statement?

A statement showing an “if and only if” relation is known as a biconditional statement. An event P will occur if and only if the event Q occurs, which means if P has occurred then it implies Q will occur and vice versa.

P: A number is divisible by 2.

Q: A number is even.

If P will occur then Q will occur and if Q will occur then P will occur.

Hence, P will occur if and only if Q will occur.

We can say that P↔Q.

Conditional Statement Examples

Q.1: If a > 0 is a positive number, then is a = 10 correct or not? Justify your answer.

Solution: Given, a > 0 and is a positive number

And it is given a = 10

So the first statement a > 0 is correct because any number greater than 0 is a positive number. But a = 10 is not a correct statement because it can be any number greater than 0.

Q.2: Justify P → Q, for the given table below.

Solution: Case 1: We can see, for the first row, in the given table,

If statement P is correct, then Q is incorrect and if Q is correct then P is incorrect. Both the statements contradict each other.

Hence, P → Q = False

Case 2: In the second row of the given table, if P is correct then Q is correct and if Q is correct then P is also correct. Hence, it satisfies the condition.

P → Q = True

Therefore, we can construct the table;

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what is statement logic

Using IF with AND, OR and NOT functions

The IF function allows you to make a logical comparison between a value and what you expect by testing for a condition and returning a result if that condition is True or False.

=IF(Something is True, then do something, otherwise do something else)

But what if you need to test multiple conditions, where let’s say all conditions need to be True or False ( AND ), or only one condition needs to be True or False ( OR ), or if you want to check if a condition does NOT meet your criteria? All 3 functions can be used on their own, but it’s much more common to see them paired with IF functions.

Technical Details

Use the IF function along with AND, OR and NOT to perform multiple evaluations if conditions are True or False.

IF(AND()) - IF(AND(logical1, [logical2], ...), value_if_true, [value_if_false]))

IF(OR()) - IF(OR(logical1, [logical2], ...), value_if_true, [value_if_false]))

IF(NOT()) - IF(NOT(logical1), value_if_true, [value_if_false]))

Here are overviews of how to structure AND , OR and NOT functions individually. When you combine each one of them with an IF statement, they read like this:

AND – =IF(AND(Something is True, Something else is True), Value if True, Value if False)

OR – =IF(OR(Something is True, Something else is True), Value if True, Value if False)

NOT – =IF(NOT(Something is True), Value if True, Value if False)

Following are examples of some common nested IF(AND()), IF(OR()) and IF(NOT()) statements. The AND and OR functions can support up to 255 individual conditions, but it’s not good practice to use more than a few because complex, nested formulas can get very difficult to build, test and maintain. The NOT function only takes one condition.

Examples of using IF with AND, OR and NOT to evaluate numeric values and text

Here are the formulas spelled out according to their logic:

Note that all of the examples have a closing parenthesis after their respective conditions are entered. The remaining True/False arguments are then left as part of the outer IF statement. You can also substitute Text or Numeric values for the TRUE/FALSE values to be returned in the examples.

Here are some examples of using AND, OR and NOT to evaluate dates.

Examples of using IF with AND, OR and NOT to evaluate dates

Using AND, OR and NOT with Conditional Formatting

You can also use AND, OR and NOT to set Conditional Formatting criteria with the formula option. When you do this you can omit the IF function and use AND, OR and NOT on their own.

From the Home tab, click Conditional Formatting > New Rule . Next, select the “ Use a formula to determine which cells to format ” option, enter your formula and apply the format of your choice.

what is statement logic

Using the earlier Dates example, here is what the formulas would be.

Example of using AND, OR and NOT as Conditional Formatting tests

Note:  A common error is to enter your formula into Conditional Formatting without the equals sign (=). If you do this you’ll see that the Conditional Formatting dialog will add the equals sign and quotes to the formula - ="OR(A4>B2,A4<B2+60)" , so you’ll need to remove the quotes before the formula will respond properly.

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what is statement logic


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  1. Statement (logic) - Wikipedia

    In logic, the term statement is variously understood to mean either: a meaningful declarative sentence that is true or false, or. a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence. In the latter case, a statement is distinct from a sentence in that a sentence is only one ...

  2. Formal logic | Definition, Examples, Symbols, & Facts

    formal logic, the abstract study of propositions, statements, or assertively used sentences and of deductive arguments. The discipline abstracts from the content of these elements the structures or logical forms that they embody.

  3. 2.1: Statements and Logical Operators - Mathematics LibreTexts

    A logical operator (or connective) on mathematical statements is a word or combination of words that combines one or more mathematical statements to make a new mathematical statement. A compound statement is a statement that contains one or more operators.

  4. Intro to Logical Statements - YouTube

    We begin our exploration into logic by analyzing LOGICAL STATEMENTS:1) Define what a logical statement is 2) Recognize examples as logical statements or not ...

  5. Examples of Logic: 4 Main Types of Reasoning | YourDictionary

    Logic is a process for making a conclusion and a tool you can use. The foundation of a logical argument is its proposition, or statement. The proposition is either accurate (true) or not accurate (false). Premises are the propositions used to build the argument. The argument is then built on premises. Then an inference is made from the premises.

  6. Logic: The concept of statement in logic and its truth value

    Logic is a process by which we arrive at a conclusion from known statements or assertions with the help of valid assumptions. The valid assumptions are known as laws of logic. The Greek philosopher and thinker Aristotle laid the foundation of the study of logic in the systematic form.

  7. A quick guide to conditional logic (article) | Khan Academy

    Diagramming conditional logic statements is an extremely useful strategy often employed by high-scoring students. However, diagramming these statements accurately—a crucial skill—can be a challenge due to the many ways that sufficient and necessary conditions can be presented in prose.

  8. Conditional Statement - Definition, Truth Table & Examples

    In the study of logic, there are two types of statements, conditional statement and bi-conditional statement. These statements are formed by combining two statements, which are called compound statements. Suppose a statement is- if it rains, then we don’t play. This is a combination of two statements.

  9. Logic Examples & Types | What is Logic? - Video & Lesson ...

    Logic is defined as a system that aims to draw reasonable conclusions based on given information. This means the goal of logic is to use data to make inferences.

  10. Using IF with AND, OR and NOT functions - Microsoft Support

    The IF function allows you to make a logical comparison between a value and what you expect by testing for a condition and returning a result if that condition is True or False. =IF (Something is True, then do something, otherwise do something else)