IIM CAT 2026 lesson summary for Logical Reasoning! Notes

1. Introduction to Propositional Logic

Propositional logic forms the foundational bedrock of rigorous mathematical reasoning and analytical problem-solving in competitive examinations like IIM CAT. A proposition is defined as a declarative statement that is either strictly True (\(T\)) or False (\(F\)), but never both simultaneously.

Let \(P\) and \(Q\) represent propositional variables. The core logical connectives used to form compound statements are defined as follows:

• Conjunction (AND): \(P \land Q\) is true only when both \(P\) and \(Q\) are true simultaneously.
• Disjunction (OR): \(P \lor Q\) is true when at least one proposition (\(P\), \(Q\), or both) is true.
• Implication (Conditional): \(P \implies Q\) represents "If \(P\), then \(Q\)." It evaluates to false ONLY when \(P\) is true and \(Q\) is false. In all other cases, it is trivially true.
• Biconditional: \(P \iff Q\) represents "\(P\) if and only if \(Q\)." It is true when both \(P\) and \(Q\) share the same truth value.```json { "optimized_title": "Propositional Logic and Deductive Reasoning - IIM CAT 2026 LRDI Chapter