Answer to Question #288674 in Discrete Mathematics for RAHUL

Question

What is mean by logic

Answer 1

Logic is concerned with statements to which the truth values, “true” and “false”, can be assigned. The purpose is to analyze these statements either individually or in collection.

Logic – Definition

A proposition is a collection of declarative statements that has either a truth value "true” or a truth value "false". A propositional consists of propositional variables and connectives. We denote the propositional variables by capital letters (A, B, etc). The connectives connect the propositional variables.

Some examples of Propositions are given below −

• "Man is Mortal", it returns truth value “TRUE”
• "12 + 9 = 3 – 2", it returns truth value “FALSE”

The following is not a Proposition −

• "A is less than 2". It is because unless we give a specific value of A, we cannot say whether the statement is true or false.

Connectives

In propositional logic generally we use five connectives which are −

• OR (∨)
• AND (∧)
• Negation/ NOT (¬)
• Implication / if-then (→)
• If and only if (⇔).

OR (∨) − The OR operation of two propositions A and B (written as A∨B

A∨B) is true if at least any of the propositional variable A or B is true.