Question

If $P,Q,R$ are subsets of a finite set then $R\times (P{}^{\prime }\cup Q{}^{\prime }){}^{\prime }$ equals

• A. $(R\times P)\cup (P\times Q)$
• B. $(R\times P)\cap (R\times Q)$
• C. $(R\times Q)\cap (P\times P)$
• D. $(R\times Q)\cup (R\times P)$

Answer 1

Answer: (B)

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

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

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