If P,Q and R are subsets of a set A , then R × (P^c cup Q^c)^c =

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2.Relations and Functions

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

A

$(R × P) \cap (R × Q)$

B

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

C

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

D

None of these

Solution

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

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

Standard 11

Mathematics

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