Track / Stage 4 / 24 of 340 #284 of 1964

Problem 284

AMC 12 late, AIME early

Combinatorics Difficulty 4.6 Find the answer

3. Let $A$ and $B$ be two distinct sets.

Proposition $p: x \in A \cap B$ ;
Proposition $q: x \in A$ or $x \in B$ .
Then $p$ is a ( ) condition for $q$ .
(A) Sufficient and necessary
(B) Sufficient but not necessary
(C) Necessary but not sufficient
(D) Neither sufficient nor necessary

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Official solution

3. B.

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