Question

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

• A. $(R\times P)\cap (R\times Q)$
• B. $(R\times Q)\cap (R\times P)$
• C. $(R\times P)\cup (R\times Q)$
• D. None of these

Answer 1

Answer: (A)

$R\times (P^C\cup Q^C{)}^C=R\times [(P^C{)}^C\cap (Q^C{)}^C]$
$=R\times (P\cap Q)=(R\times P)\cap (R\times Q)$