First slide

Introduction to Sets

Question

If P, Q and R are subsets of a set A, then $R \times {(P^{c} \cup Q^{c})}^{c}$

Easy

A

$(R \times P) \cap (R \times Q)$
B

$(R \times Q^{c}) \cap (R \times P)$
C

$(R \times P) \cup (R \times Q)$
D

None of these

Solution

$\begin{array}{l} R \times {(P^{c} \cup Q^{c})}^{c} = R \times [{(P^{c})}^{c} \cap {(Q^{c})}^{c}] \\ = R \times (P \cap Q) = (R \times P) \cap (R \times Q) = (R \times Q) \cap (R \times P) \end{array}$

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