Mathematical__logic__Class__notes

Unit 2 - Mathematical Logic

Propositional 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 a composite manner.

Prepositional 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 sun rises in the East and sets in the West, it returns truth value
“TRUE”
 1 + 1 = 2, it returns truth value “TRUE”
 'b' is a vowel.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 (¬/~)
 NAND
 NOR
 Implication / if-then (→)
 If and only if (⇔)