Discussion
Let \(A\) and \(B\) be two subsets of a universal set \(U\). If \(n(U) = 116\), \(N(A \cup B) = 99\), \(n(B) = 61\) and \(n(A \cap B) = 28\), then \(n(A')\) is equal to
Answer: E
\(n(A') = 50\).
First find \(n(A)\) from the union formula, then subtract it from the universal set.
\[ \begin{aligned} n(A \cup B) &= n(A) + n(B) - n(A \cap B) \\ 99 &= n(A) + 61 - 28 \\ n(A) &= 66 \\ n(A') &= 116 - 66 = 50 \end{aligned} \]
Check: \(66 + 61 - 28 = 99\), as given. The common slip is to subtract \(n(A \cup B)\) or \(n(B)\) from 116 directly; \(116 - 61 = 55\) and \(116 - 99 = 17\) are not \(n(A')\), because \(A'\) contains the part of \(B\) outside \(A\) as well as everything outside both sets.
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