Discussion
Let \(X = \{a, b, c, d, e\}\) and \(A = \{a, b, c, d, \}\) . Let \(P = \{B : B \subseteq X \text{ and } A \setminus B = \{d\}\}\) . Then the number of elements in the set P , is
Answer: B
P has 2 elements.
\(A \setminus B = \{d\}\) means that, of the elements of A, only d is missing from B. So B must contain a, b and c, and must not contain d. The only element of X still undecided is e, which B may or may not contain:
\[ P = \{\{a, b, c\},\ \{a, b, c, e\}\} \]
So P has 2 elements. Counting all subsets of X (32), or treating e as forced in or out, leads to the wrong totals such as 1, 4 or 8.
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