IIM CAT 2026 cheat sheet for Logical Reasoning! 📱 Practice 1 Lakh+ PYQs on ExamBhai.com! - Free Study Material

Chapter Summary: Logical Reasoning for CAT 2026

Logical Reasoning (LR) tests structural thinking, pattern recognition, and analytical constraint mapping. Below is a structured reference guide covering essential core concepts and formulas commonly tested in the CAT LR section.

1. Arrangement & Distribution Principles

Linear and circular arrangements rely on fixed constraints and relational positions. For circular arrangements with \(n\) distinct entities:

• Number of circular permutations (facing center): \((n - 1)!\)
• Number of circular permutations (undirected, e.g., necklaces): \(\frac{(n - 1)!}{2}\)

2. Set Theory & Venn Diagrams

Multi-variable set problems require tracking intersections and union boundaries across sets. For a three-set Venn Diagram (Sets \(A\), \(B\), and \(C\)):

\[n(A \cup B \cup C) = n(A) + n(B) + n(C) - [n(A \cap B) + n(B \cap C) + n(C \cap A)] + n(A \cap B \cap C)\]

For maxima and minima set problems, express intersecting regions as non-negative variables and solve using inequality bounds under the universal set constraint \(U\).

3. Networks, Paths, & Binary Logic

Binary logic involves statements by Truth-Tellers (always speak truth), Liars (always lie), and Alternators (alternate truth and lies).

• Contradiction Principle: If two statements directly contradict each other, exactly one must be true and one must be false.
• Implication Equivalence: An implication statement \(P \to Q\) is logically equivalent to its contrapositive \(\neg Q \to \neg P\).

4. Tournament Mechanics

In Knockout tournaments with \(n\) players, the total number of matches required to declare a single champion is \(n - 1\). In a Round-Robin tournament where every team plays every other team once:

\[\text{Total Matches} = \frac{n(n - 1)}{2}\]