CAT Venn Diagrams: Logic for DILR & Quant

Venn Diagrams are essential for CAT, appearing in both Quant (Set Theory) and DILR (Caselets). This guide covers the core formulas for 2 and 3 sets, plus the visual strategies needed to solve complex maximization/minimization problems without algebra.

Section 1: The Core Concepts

Foundation: Union & Intersection

Start with the fundamental definitions of sets. Understand the difference between 'Union' (OR) and 'Intersection' (AND) to decode word problems correctly.

The Core Formula: Inclusion-Exclusion (2 Sets)

Master the formula for two sets. Learn why we subtract the intersection to avoid the 'double-counting trap' common in CAT Arithmetic.

The Inclusion-Exclusion Principle (3 Sets)

Extend the logic to three sets. Understand the critical step of adding back the central intersection, a key concept for DILR caselets.

Section 2: Visual Solving Strategies

Visual Method: The Two-Set Diagram

Move beyond formulas. Learn to map data into the four distinct regions of a Venn diagram to solve problems faster and with fewer errors.

Advanced: The Three-Set Diagram

Level up to the 8-region diagram. This visual tool is indispensable for solving complex 3-variable DILR sets involving 'Only A', 'Only B', etc.

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