Question

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

• A. $\left(RxP\right)\cap \left(RxQ\right)$
• B. $\left(RxQ\right)\cap \left(RxP\right)$
• C. $\left(RxP\right)\cup \left(RxQ\right)$
• D. None of these

Answer 1

The correct option is B

$\left(RxQ\right)\cap \left(RxP\right)$

Explanation for the correct option

If$P,Q\mathrm{and}R$ are subsets of the set $A$ then

$$\begin{gathered} \Rightarrow R\times {(P^c\cup Q^c)}^c \\ \Rightarrow R\times [{\left(P^c\right)}^c\cup {\left(Q^c\right)}^c] \\ \Rightarrow R\times (P\cap Q) \\ \Rightarrow (R\times Q)\cap (R\times P) \end{gathered}$$

Hence option ‘B’ is correct.