Assertion & Reasoning (with Venn / Syllogism)

Venn Diagrams (set counting)

Two sets: $n(A\cup B) = n(A) + n(B) - n(A\cap B)$; exactly one $= n(A)+n(B) - 2n(A\cap B)$; neither $= \text{Total} - n(A\cup B)$.

Three sets (what exams test):

• Only A $= n(A) - n(A\cap B) - n(A\cap C) + n(A\cap B\cap C)$
• Exactly two $= n(A\cap B) + n(B\cap C) + n(A\cap C) - 3\,n(A\cap B\cap C)$
• At least two $= n(A\cap B) + n(B\cap C) + n(A\cap C) - 2\,n(A\cap B\cap C)$
• None $= \text{Total} - n(A\cup B\cup C)$

Trap: when a question gives the pairwise overlaps and the triple overlap, subtract the triple out before answering "exactly two".

Syllogism shapes: All A are B → A inside B · No A is B → separate circles · Some A are B → partial overlap.

Assertion – Reasoning Logic

Standard option key:

• (A) Both true, and R correctly explains A
• (B) Both true, but R does not explain A
• (C) A true, R false
• (D) A false, R true
• (E) Both false

Trap patterns: (1) true-but-irrelevant R — ask "could I derive A from R alone?"; if not, it's (B). (2) sounds-right-but-factually-wrong R — check R's truth before its relevance. (3) reversed causality → still (B). (4) partial truth — if R holds only in some contexts, treat it as false.