Question 50

Let $$P$$ and $$Q$$ be two distinct nonempty sets. Then $$(P \cup Q)^c \cup (P^c \cap Q)$$ equals

Solution

$$(P \cup Q)^c \cup (P^c \cap Q)$$ = $$\left(P^c\cap Q^c\right)\cup(P^c\cap Q)\ =\ P^c\cap\left(Q^cUQ\right)$$

= $$\ P^c\cap universal\ set$$

= $$\ P^c$$

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