Question

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

• 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. $Noneofthese$

Answer 1

Answer: (A), (B)

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

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