Logical Reasoning Cheat Sheet - IIM CAT 2026

Welcome to the ultimate chapter-wise study guide for IIM CAT 2026 Logical Reasoning. Logical Reasoning and Data Interpretation (DILR) is one of the most critical sections in the CAT exam. Master fundamental propositional logic, logical equivalences, valid syllogism argument forms, common logical fallacies, and quantifiers to maximize your percentile score.

CAT LR PYQ Analysis & Weightage

In the recent CAT exam patterns, formal logic concepts form the core underlying structure of complex arrangements, binary logic, truth-teller/liar sets, and deduction-based reasoning puzzles. Mastering fundamental connectives and inference rules ensures rapid problem solving without falling into trap choices.

Chapter 1: Propositional Logic

Propositional logic analyzes statements that carry a truth value (either True or False). Basic logical connectives define the fundamental relationships between simple statements:

• Negation (\( eg p\)): NOT \(p\). Inverts the truth value of statement \(p\).
• Conjunction (\(p \land q\)): \(p\) AND \(q\). True only when both \(p\) and \(q\) are True.
• Disjunction (\(p \lor q\)): \(p\) OR \(q\). True when at least one of \(p\) or \(q\) is True.
• Implication (\(p \to q\)): If \(p\), then \(q\). False ONLY when \(p\) is True and \(q\) is False.
• Biconditional (\(p rightarrow q\)): \(p\) if and only if \(q\). True when both statements have identical truth values.

Truth Table Reference

Chapter 2: Logical Equivalences

Understanding logical equivalences allows candidates to rewrite complex condition statements into simpler forms during time-pressured CAT sets.

• Contrapositive: \(p \to q \equiv eg q \to eg p\) (Always logically equivalent to the original implication).
• Converse: \(q \to p\) (Not logically equivalent to the original implication).
• Inverse: \( eg p \to eg q\) (Logically equivalent to the Converse, but not the original implication).
• De Morgan's Laws:\[ eg(p \land q) \equiv eg p \lor eg q\]\[ eg(p \lor q) \equiv eg p \land eg q\]
• Implication Law:\[p \to q \equiv eg p \lor q\]

Chapter 3: Syllogisms & Valid Argument Forms

Syllogistic logic forms valid deductive argument structures essential for CAT critical reasoning and deduction sets:

• Modus Ponens: Given \(p \to q\) and \(p\), we validly infer \(q\).
• Modus Tollens: Given \(p \to q\) and \( eg q\), we validly infer \( eg p\).
• Hypothetical Syllogism: Given \(p \to q\) and \(q \to r\), we validly infer \(p \to r\).
• Disjunctive Syllogism: Given \(p \lor q\) and \( eg p\), we validly infer \(q\).

Chapter 4: Common Logical Fallacies

Fallacies represent invalid deductive steps that frequently appear as trap options in CAT DILR questions:

• Affirming the Consequent: Invalidly concluding \(p\) from \((p \to q)\) and \(q\).
• Denying the Antecedent: Invalidly concluding \( eg q\) from \((p \to q)\) and \( eg p\).

Chapter 5: Universal & Existential Quantifiers

Quantifiers express the scope of logical statements across domains:

• Universal Quantifier (\(\forall\)): "For all" — represented as \(\forall x P(x)\).
• Existential Quantifier (\(\exists\)): "There exists" — represented as \(\exists x P(x)\).
• Negation Rules for Quantifiers:\[ eg(\forall x P(x)) \equiv \exists x eg P(x)\]\[ eg(\exists x P(x)) \equiv \forall x eg P(x)\]

People Also Ask (FAQs)

What is the difference between Converse and Contrapositive in CAT Logical Reasoning?

For an implication statement \(p \to q\), the Contrapositive is \( eg q \to eg p\) and is always logically equivalent to the original statement. The Converse is \(q \to p\), which is NOT logically equivalent to the original statement.

How are De Morgan's Laws used in CAT DILR puzzles?

De Morgan's Laws allow you to negate complex conditions involving AND/OR statements. For instance, the negation of "Both A and B are present" (\( eg(A \land B)\)) is "Either A is not present or B is not present" (\( eg A \lor eg B\)).

What is Affirming the Consequent fallacy?

Affirming the Consequent is an invalid logical deduction where one assumes that because the consequence \(q\) is true, the condition \(p\) must also be true given \(p \to q\).