Track / Stage 4 / 20 of 340 #280 of 2000

Problem 280

AMC 12 late, AIME early

Combinatorics Difficulty 4.5 Find the answer

Example 1. $A \cap B=\phi, M=\{A$ 's subsets $\}$ .
$N=\{B$ 's subsets $\}$ , then
(A) $M \cap N=\phi ; \quad(B) M \cap N=\{\phi\}$ ;
(C) $M \cap N=A \cap B$ ;
(D) $M \cap N \subset A \cap B$ .

Your answer

Official solution

Students may mistakenly think that $A$ and $B$ have no common elements, and thus their subsets also have no common elements, leading them to choose (A) and (C). In fact, $\phi \in M, \phi \in N$ , so the correct choice is (B).

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.