Set A contains m elements. B and C are two subsets of A such that n(B) = n(C), B union C = A, and n(B intersection C) = 1. Identify the correct statement(s).

Question

Accepted Answer

m must be odd. From n(B union C)=m and n(B)=n(C)=k, n(B cap C)=1: m=2k-1, so m must be odd. The number of (ordered) ways to form B and C: choose the 1 element in B cap C (m ways), then split remaining m-1 elements into two equal groups of (m-1)/2 each: C(m-1,(m-1)/2) ways. Total = m * C(m-1,(m-1)/2). If B and C are unordered (B,C same as C,B), divide by 2 but since B and C are labeled subsets, the ordered count applies.

Set A contains m elements. B and C are two subsets of A such that n(B) = n(C), B union C = A, and n(B intersection C) = 1. Identify the correct statement(s).

Solution

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