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

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Logical Reasoning Core Concepts & Formulae

A comprehensive chapter-wise review of essential logical structures, arrangements, and analytical principles for CAT 2026 preparation.

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1. Linear & Circular Arrangements

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Arrangements form the baseline of analytical sets. For \(n\) distinct entities in a row, the total number of linear arrangements is \(n!\). For circular arrangements of \(n\) distinct items where direction matters, the total arrangements are \((n-1)!\); if clockwise and counter-clockwise orientations are identical, it is \(\frac{(n-1)!}{2}\).

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• Facing Direction: In circular setups, if all face the center, Left is clockwise and Right is counter-clockwise. Reverse both if facing outward.
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• Constrained Positioning: If \(k\) items must always sit together, treat them as a single block giving \((n-k+1)! \times k!\) linear arrangements.
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2. Matrix Grid & Matching Puzzles

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Matching problems map attributes across multiple categories (e.g., Person, Profession, City). Use a standard grid representation to eliminate invalid combinations systemically.

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• Degree of Freedom: Identify fixed anchor variables first to reduce grid complexity.
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• Conditional Rules: Convert conditions like "A goes only if B goes" into formal logic: \(A \to B\), with contrapositive \(\neg B \to \neg A\).
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3. Set Theory & Venn Diagrams

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For sets involving 2 or 3 overlapping variables, the Inclusion-Exclusion Principle dictates total coverage:

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

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For exact allocations, let \(E_1, E_2, E_3\) represent elements belonging to exactly one, two, or three sets respectively:

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\[\text{Total} = E_1 + E_2 + E_3 + \text{None}\]

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\[n(A)+n(B)+n(C) = E_1 + 2E_2 + 3E_3\]

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4. Binary Logic & Truth-Teller Puzzles

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Puzzles involve Truth-Tellers (always state truth), Liars (always state falsehoods), and Alternators (alternate between truth and lie).

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• Contradiction Rule: If Person A states "Person B is a liar" and Person B states "Person A is a liar", at least one is lying.
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• Self-Reference: A Truth-Teller can never say "I am a liar". An Alternator's state depends entirely on the truthfulness of their previous statement.
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5. Tournaments & Games

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In a single round-robin tournament with \(n\) teams, total matches played equal \(\binom{n}{2} = \frac{n(n-1)}{2}\). For a knock-out tournament with \(n\) teams, exactly \(n-1\) matches are required to determine a single winner.

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