If $$P$$ and $$Q$$ are two subsets of a set $$S$$ then $$(P - Q) \cup (Q - P)$$ is equal to

Solution

$$(P - Q) \cup (Q - P)$$ is the set of elements in exactly one of $$P$$, $$Q$$. Since $$P - Q = P \cap Q'$$ and $$Q - P = P' \cap Q$$, option a is this set. Elements in $$P \cup Q$$ but not in $$P \cap Q$$ give option b, which equals option c, and by De Morgan $$P' \cup Q' = (P \cap Q)'$$, so option d is the same set. All four options a, b, c and d are correct.

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