A universal​ set, with​ n(U) = ​112, is partitioned into three​ subsets: A,​ B, and C. If​ n(B) = ​5⋅n(A), and​ n(C) = 2​⋅n(B), find the number of elements in the subset A.

Answer 1

Well suppose n(A) = x

then n(B) = 5x

and n(C) = 2 x 5x = 10x

So n(A) + n(B) + n(C) = 16x, and assuming sets are distinct 16x = 112, so x = 112 / 16 = 7.

So n(A) = 7.

Mike