- Entertainment & Pop Culture
- Geography & Travel
- Health & Medicine
- Lifestyles & Social Issues
- Philosophy & Religion
- Politics, Law & Government
- Sports & Recreation
- Visual Arts
- World History
- On This Day in History
- Biographies
- Top Questions
- Week In Review
- Infographics
- Demystified
- Image Galleries
- One Good Fact
- Britannica Explains In these videos, Britannica explains a variety of topics and answers frequently asked questions.
- Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.
- #WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.
- This Time in History In these videos, find out what happened this month (or any month!) in history.
- Demystified Videos In Demystified, Britannica has all the answers to your burning questions.
- Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.
- COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.
- 100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.
- Britannica Beyond We’ve created a new place where questions are at the center of learning. Go ahead. Ask. We won’t mind.
- Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century. Learn about the major environmental problems facing our planet and what can be done about them!
- SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!
- Introduction

## General observations

- Formation rules for PC
- Validity in PC
- Interdefinability of operators
- Axiomatization of PC
- Partial systems of PC
- Nonstandard versions of PC
- Natural deduction method in PC
- Validity in LPC
- Logical manipulations in LPC
- Classification of dyadic relations
- Axiomatization of LPC
- Semantic tableaux
- Special systems of LPC
- Definite descriptions
- Higher-order predicate calculi
- Alternative systems of modal logic
- Validity in modal logic
- Facts & Related Content
- More Articles On This Topic
- Additional Reading
- Contributors
- Article History

## formal logic

Our editors will review what you’ve submitted and determine whether to revise the article.

- school Campus Bookshelves
- menu_book Bookshelves
- perm_media Learning Objects
- login Login
- how_to_reg Request Instructor Account
- hub Instructor Commons
- Download Page (PDF)
- Download Full Book (PDF)
- Periodic Table
- Physics Constants
- Scientific Calculator
- Reference & Cite
- Tools expand_more
- Readability

selected template will load here

## 2.1: Statements and Logical Operators

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

- The conjunction of the statements \(P\) and \(Q\) is the statement “\(P\) and \(Q\)” and its denoted by \(P \wedge Q\). The statement \(P \wedge Q\) is true only when both \(P\) and \(Q\) are true.
- The disjunction of the statements \(P\) and \(Q\) is the statement “\(P\) or \(Q\)” and its denoted by \(P \vee Q\). The statement \(P \vee Q\) is true only when at least one of \(P\) or \(Q\) is true.
- The negation ( of a statement ) of the statement \(P\) is the statement “ not \(P\) ” and is denoted by \(\urcorner P\). The negation of \(P\) is true only when \(P\) is false, and \(\urcorner P\) is false only when \(P\) is true.
- The implication or conditional is the statement “ If \(P\) then \(Q\)” and is denoted by \(P \to Q\). The statement \(P \to Q\) is often read as “\(P\) implies \(Q\), and we have seen in Section 1.1 that \(P \to Q\) is false only when \(P\) is true and \(Q\) is false.

- The negation of the statement, “391 is prime” is “391 is not prime.”
- The negation of the statement, “\(12 < 9\)” is “\(12 \ge 9\).”

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

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

(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.

## Other Forms of Conditional Statements

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

- If \(P\), then \(Q\).
- \(P\) implies \(Q\).
- \(P\) only if \(Q\).
- \(Q\) if \(P\).
- Whenever \(P\) is true, \(Q\) is true.
- \(Q\) is true whenever \(P\) is true.
- \(Q\) is necessary for \(P\). (This means that if \(P\) is true, then \(Q\) is necessarily true.)

## Progress Check 2.1: The "Only if" 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

- For a truth table with two different simple statements, four rows are needed since there are four different combinations of truth values for the two statements. We should be consistent with how we set up the rows. The way we will do it in this text is to label the rows for the first statement with (T, T, F, F) and the rows for the second statement with (T, F, T, F). All truth tables in the text have this scheme.
- For a truth table with three different simple statements, eight rows are needed since there are eight different combinations of truth values for the three statements. Our standard scheme for this type of truth table is shown in Table 2.2 .

- When completing the column for \(P \wedge \urcorner Q\), remember that the only time the conjunction is true is when both \(P\) and \(\urcorner Q\) are true.
- When completing the column for \((P \wedge \urcorner Q) \to R\), remember that the only time the conditional statement is false is when the hypothesis \((P \wedge \urcorner Q)\) is true and the conclusion, \(R\), is false.

## Progress Check 2.2: Constructing Truth Tables

Construct a truth table for each of the following statements:

- \(P \wedge \urcorner Q\)
- \(\urcorner(P \wedge Q)\)
- \(\urcorner P \wedge \urcorner Q\)
- \(\urcorner P \vee \urcorner Q\)

Do any of these statements have the same truth table?

## The Biconditional Statement

## Progress Check 2.3: The Truth Table for the Biconditional Statement

## Other Forms of the Biconditional Statement

- \(P\) is and only if \(Q\).
- \(P\) is necessary and sufficient for \(Q\).
- \(P\) implies \(Q\) and \(Q\) implies \(P\).

Tautologies and Contradictions

## Definition: tautology

## Progress Check 2.4 (Tautologies and Contradictions)

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

- Use a truth table to show that \((P \vee \urcorner P)\) is a tautology.
- Use a truth table to show that \((P \wedge \urcorner P)\) is a contradiction.
- Use a truth table to determine if \(P \to (P \vee P)\) is a tautology, a contradiction, nor neither.

## Exercises for Section 2.1

- Suppose that Daisy says, “If it does not rain, then I will play golf.” Later in the day you come to know that it did rain but Daisy still played golf. Was Daisy’s statement true or false? Support your conclusion.
- Suppose that \(P\) and \(Q\) are statements for which \(P \to Q\) is true and for which \(\urcorner Q\) is true. What conclusion (if any) can be made about the truth value of each of the following statements? (a) \(P\) (b) \(P \wedge Q\) (c) \(P \vee Q\)
- Suppose that \(P\) and \(Q\) are statements for which \(P \to Q\) is false. What conclusion (if any) can be made about the truth value of each of the following statements? (a) \(\urcorner P \to Q\) (b) \(Q \to P\) (c) \(P \ vee Q\)
- Suppose that \(P\) and \(Q\) are statements for which \(Q\) is false and \(\urcorner P \to Q\) is true (and it is not known if \(R\) is true or false). What conclusion (if any) can be made about the truth value of each of the following statements? (a) \(\urcorner Q \to P\) (b) \(P\) (c) \(P \wedge R\) (d) \(R \to \urcorner P\)
- Construct a truth table for each of the following statements: (a) \(P \to Q\) (b) \(Q \to P\) (c) \(\urcorner P \to \urcorner Q\) (d) \(\urcorner Q \to \urcorner P\) Do any of these statements have the same truth table?
- Construct a truth table for each of the following statements: (a) \(P \vee \urcorner Q\) (b) \(\urcorner (P \vee Q)\) (c) \(\urcorner P \vee \urcorner Q\) (d) \(\urcorner P \wedge \urcorner Q\) Do any of these statements have the same truth table?
- Construct truth table for \(P \wedge (Q \vee R)\) and \((P \wedge Q) \vee (P \wedge R)\). What do you observe.
- Laura is in the seventh grade.
- ��Laura got an A on the mathematics test or Sarah got an A on the mathematics test.
- ��If Sarah got an A on the mathematics test, then Laura is not in the seventh grade. If possible, determine the truth value of each of the following statements. Carefully explain your reasoning. (a) Laura got an A on the mathematics test. (b) Sarah got an A on the mathematics test. (c) Either Laura or Sarah did not get an A on the mathematics test.
- Let \(P\) stand for “the integer \(x\) is even,” and let \(Q\) stand for “\(x^2\) is even.” Express the conditional statement \(P \to Q\) in English using (a) The "if then" form of the conditional statement (b) The word "Implies" (c) The "only if" form of the conditional statement (d) The phrase "is necessary for" (e) The phrase "is sufficient for"
- Repeat Exercise (9) for the conditional statement \(Q \to P\).
- For statements \(P\) and \(Q\), use truth tables to determine if each of the following statements is a tautology, a contradiction, or neither. (a) \(\urcorner Q \vee (P \to Q)\). (b) \(Q \wedge (P \wedge \urcorner Q)\). (c) \((Q \wedge P) \wedge (P \to \urcorner Q)\). (d) \(\urcorner Q \to (P \wedge \urcorner P)\).
- For statements \(P\), \(Q\), and \(R\): (a) Show that \([(P \to Q) \wedge P] \to Q\) is a tautology. Note : In symbolic logic, this is an important logical argument form called modus ponens . (b) Show that \([(P \to Q) \wedge (Q \to R)] \to (P \to R)\) is atautology. Note : In symbolic logic, this is an important logical argument form called syllogism . Explorations and Activities
- Working with Truth Values of Statements. Suppose that \(P\) and \(Q\) are true statements, that \(U\) and \(V\) are false statements, and that \(W\) is a statement and it is not known if \(W\) is true or false. Which of the following statements are true, which are false, and for which statements is it not possible to determine if it is true or false? Justify your conclusions. (a) \((P \vee Q) \vee (U \wedge W)\) (f) \((\urcorner P \vee \urcorner U) \wedge (Q \vee \urcorner V)\) (b) \(P \wedge (Q \to W)\) (g) \((P \wedge \urcorner Q) \wedge (U \vee W)\) (c) \(P \wedge (W \to Q)\) (h) \((P \vee \urcorner Q) \to (U \wedge W)\) (d) \(W \to (P \wedge U)\) (i) \((P \vee W) \to (U \wedge W)\) (e) \(W \to (P \wedge \urcorner U)\) (j) \((U \wedge \urcorner V) \to (P \wedge W)\)

- Words with Friends Cheat
- Wordle Solver
- Word Unscrambler
- Scrabble Dictionary
- Anagram Solver
- Wordscapes Answers

Sign up for our weekly newsletters and get:

By signing in, you agree to our Terms and Conditions and Privacy Policy .

We'll see you in your inbox soon.

## Examples of Logic: 4 Main Types of Reasoning

## Definitions of Logic

“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.

- 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.
- Finally, a conclusion is drawn.

## Definition of Logic in Philosophy

## Definition of Logic in Mathematics

## Types of Logic With Examples

Generally speaking, there are four types of logic.

## Informal Logic

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.

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.

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

## Formal Logic

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

- Propositions: If all mammals feed their babies milk from the mother (A). If all cats feed their babies mother’s milk (B). All cats are mammals(C). The Ʌ means “and,” and the ⇒ symbol means “implies.”
- Conclusion: A Ʌ B ⇒ C
- Explanation: Proposition A and proposition B lead to the conclusion, C. If all mammals feed their babies milk from the mother and all cats feed their babies mother’s milk, it implies all cats are mammals.

## Mathematical Logic

## Types of Reasoning With Examples

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

## Deductive Reasoning Examples

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.

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

Conclusion: The oak tree has a trunk.

## Inductive Logic Examples

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

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.

## Follow the Logic

## Statement in Logic

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

- The truth or falsity of a statement is called the truth value of the statement.
- If the statement is true then its truth value is denoted by the letter ‘T’. If the statement is false then its truth value is denoted by the letter ‘F’. In boolean algebra 1 is used for T and 0 is used for F.

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.

- Do your homework today : It is a command or suggestion. Hence it is not a statement.
- x 2 – 5x + 6 = 0 , when x = 2: It is a statement. Its truth value is ‘T’
- x 2 – 5x + 6 = 0, x ∈ R : For x = 2 or x = 3 it is true for x ≠ 2 and x ≠ 3, it is false. Hence it is open sentence. It is not a statement.
- It is white in colour.: We cannot decide whether the statement is true or false. It is not a statement.
- x + 3 = 5 : If x = 2 it is true and if x ≠ 2 it is false. Hence it is open sentence. It is not a statement.
- Oh! What a beautiful scene! : It is an exclamation. Hence it is not a statement.
- Let us go for a walk: It is a suggestion. Hence it is not a statement.
- I wish the man had wings : It is a wish. Hence it is not a statement.
- Please give me a glass of water: It is a request i.e. imperative sentence. Hence it is not a statement.
- Get out of the class immediately: It is a Command i.e. imperative sentence. Hence it is not a statement.
- When is your examination going to start? : It is an interrogative sentence. Hence it is not a statement.
- The sum of two odd integers is always odd : It is a statement. Its truth value is ‘F’
- The product of two odd integers is always odd : It is a statement. Its truth value is ‘T’
- Please come here : It is request i.e. imperative sentence. Hence it is not a statement.
- The quadratic equation x 2 – 3x + 2 = 0 has two real roots : It is a statement. Its truth value is ‘T’
- The square of any real number is always positive : It is a statement. Its truth value is ‘F’. Because the square of 0 is 0 which is neither positive nor negative.
- 5 + 4 = 11 : It is a statement. Its truth value is ‘F’
- Every square of an odd number is always even : It is a statement. Its truth value is ‘F’
- 1 is a prime number : It is a statement. Its truth value is ‘F’
- Every natural number is a whole number : It is a statement. Its truth value is ‘T’
- Are you ready for a picnic? : It is an interrogative sentence. Hence it is not a statement.
- Sin 2θ = 2 sin θ cos θ, for all θ : It is a statement. Its truth value is ‘T’
- 829 is divisible by 9 : It is a statement. Its truth value is ‘F’
- What a great fall of Humpty Dumpty! : It is an exclamatory sentence. Hence it is not a statement.
- New Delhi is the capital of India : It is a statement. Its truth value is ‘T’
- Shut the door : It is an imperative sentence. Hence it is not a statement.
- Please give me a pen: It is an imperative sentence. Hence it is not a statement.
- Do you like fruits? : It is an interrogative sentence. Hence it is not a statement.
- What a heavy downpour! : It is an exclamatory sentence. Hence it is not a statement.
- Have you ever seen a rainbow? : It is an interrogative sentence. Hence it is not a statement.
- x + 2 = 7 : It is true when x = 5 and false when x ≠ 5. It is an open sentence. Hence it is not a statement.
- He is a musician: Its truth cannot be determined. Hence it is not a statement.
- Statistics is an easy subject : Its truth cannot be determined because it is a perception which may change from person to person. Hence it is not a statement.
- The sun is a star : It is a statement. Its truth value is ‘T’
- May God bless you! : It is a wish. Hence it is not a statement.
- The sum of the interior angles of a triangle is 180° : It is a statement. Its truth value is ‘T’
- Every real number is a complex number : It is a statement. Its truth value is ‘T’. because every real number can be written in the form a + bi
- Why are you upset? : It is an interrogative sentence. Hence it is not a statement.
- The square root of – 9 is a rational number : It is a statement. Its truth value is ‘F’
- The sum of cube roots of unity is 1 : It is a statement. Its truth value is ‘F’. Because the sum is zero.
- x 2 – 3x + 2 implies that x = -1 or x = -2 : It is a statement. Its truth value is ‘T’
- He is a good person : Its truth value cannot be determined because it is a perception which may change from person to person. Hence it is not a statement.
- Two is the only even prime number : It is a statement. Its truth value is ‘T’
- Do not disturb : It is an imperative sentence. Hence it is not a statement.
- x 2 – 3x – 4 = 0 when x = -1: It is a statement. Its truth value is ‘F’
- It is red in colour : We cannot decide whether the sentence is true or false. Hence it is not a statement.
- Every parallelogram is a rhombus: It is a statement. Its truth value is ‘F’.
- Every set is a finite set : It is a statement. Its truth value is ‘F’
- Indians are intelligent : Its truth value cannot be determined because it is a perception which may change from person to person. Hence it is not a statement.
- Do your work properly : It is a suggestion. Hence it is not a statement.
- x + 3 = 10 : It is true when x = 7 and false when x ≠ 7. It is an open sentence. Hence it is not a statement.
- Will you help me? : It is an imperative sentence. Hence it is not a statement.
- Square of an odd number is odd : It is a statement. Its truth value is ‘T’
- Zero is a complex number: It is a statement. Its truth value is ‘T’. Because any real number is a complex number.
- All real numbers are rational numbers: It is a statement. Its truth value is ‘F’
- 2 + 3 < 6 : It is a statement. Its truth value is ‘T’
- x 2 – 5x + 6 = 0 when x = 2 : It is a statement. Its truth value is ‘T’.
- The door is open : Its truth cannot be determined because it is a perception (How much?) which may change from person to person. Hence it is not a statement.
- I am lying : Its truth cannot be determined because it is dependent on the truthfulness of the person saying it. Hence it is not a statement. It is called the liar’s paradox.

## Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

## Unit 1: Lesson 11

- Conditional reasoning and logical equivalence
- If X, then Y | Sufficiency and necessity
- The Logic of "If" vs. "Only if"

## A quick guide to conditional logic

- If Joan had gotten an A on her paper, she could pass the course without doing the presentation.
- People can feel secure if they are governed by laws that are not vague.
- Knowledge can be gained only if medical consent is sometimes bypassed.
- Only propositions that can be proven true can be known to be true.
- Any moon, by definition, orbits a planet.
- Every student who walks to school goes home for lunch.
- No strictly physical theory can explain consciousness.
- Fitness consultants who smoke cigarettes cannot help their clients become healthier.
- Without self-understanding it is impossible to understand others.
- Novelists require some impartiality to get an intuitive grasp of the motions of everyday life.
- In order to understand Stuart’s art, Robbins must be able to pass judgment on it.
- The existence of a moral order depends upon human souls being immortal.
- Inflation occurs whenever the money supply grows more than the production of goods and services grows.
- Ann would not quit unless she were offered a fellowship.
- Conditional logic shows up in some Analytical Reasoning rules and some Logical Reasoning passages. Strength and confidence in this area can give you an edge on Test Day.
- Refer back to this article often if you find yourself mistranslating statements. If you are the type of student who works well with flashcards, go ahead and make flashcards from this article!
- Translate the logical meaning of statements—don't translate word by word without considering whether the logic matches the sufficient and necessary conditions you've chosen.
- Trigger (the condition on the left) and Result (the condition on the right) simply means that if I know that the condition on the left is true, then I 100% also know that the condition on the right is true (it already happened, is happening, or will happen). Timeline doesn't matter in conditional logic. The only thing that matters is which event is sufficient to get to which other event.
- Conditional logic takes time and practice. It's like learning a new language. Be patient, don't just give up and guess, and keep working through our other logic articles and video lessons until it all "clicks".
- Lastly, get in the habit of reading our explanations carefully to learn if you've mistranslated something.

## Want to join the conversation?

## Conditional Statement

## Conditional Statement Definition

- A conditional statement is also called implication .
- The sign of the logical connector conditional statement is →. Example P → Q pronouns as P implies Q.
- The state P → Q is false if the P is true and Q is false otherwise P → Q is true.

## Truth Table for Conditional Statement

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

- If A is true, that is, it is raining and B is false, that is, we played, then the statement A implies B is false.
- If A is false, that is, it is not raining and B is true, that is, we did not play, still the statement is true. A is the necessary condition for B but it is not sufficient.
- If A is true, B should be true but if A is false B may or may not be true.

## What is a Bi-Conditional Statement?

P: A number is divisible by 2.

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.

## 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

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

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

Therefore, we can construct the table;

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Visit BYJU’S for all Maths related queries and study materials

## Register with BYJU'S & Download Free PDFs

## Using IF with AND, OR and NOT functions

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

## Technical Details

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]))

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)

Here are the formulas spelled out according to their logic:

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

## Using AND, OR and NOT with Conditional Formatting

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

## Need more help?

You can always ask an expert in the Excel Tech Community or get support in the Answers community .

Learn how to use nested functions in a formula

Excel functions (alphabetical)

## IMAGES

## VIDEO

## COMMENTS

In logic, the term statement is variously understood to mean either:

a meaningful declarative sentence that is true or false,or. aproposition. 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 ...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 orlogicalforms that they embody.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.We begin our exploration into

logicby analyzingLOGICAL STATEMENTS:1) Define what alogicalstatementis 2) Recognize examples aslogical statementsor not ...Logicis a process for making a conclusion and a tool you can use. The foundation of alogicalargument is its proposition, orstatement. 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.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.Diagramming conditional

logicstatementsis an extremely useful strategy often employed by high-scoring students. However, diagramming thesestatementsaccurately—a crucial skill—can be a challenge due to the many ways that sufficient and necessary conditions can be presented in prose.In the study of

logic, there are two types ofstatements, conditionalstatementand bi-conditionalstatement. Thesestatementsare formed by combining twostatements, which are called compoundstatements. Suppose astatementis- if it rains, then we don’t play. This is a combination of twostatements.Logicis defined as a system that aims to draw reasonable conclusions based on given information. This means the goal oflogicis to use data to make inferences.The IF function allows you to make a

logicalcomparison 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)