State whether the given statement is true or false:
P $\cap$ (Q $\cup$ R) = (P $\cap$ Q) $\cup$ R

True

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False

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Solution

The correct option is B False
For the LHS:
$P \cap (Q \cup R) = (P \cap Q) \cup (P \cap R)$ ...as intersection distributes over union
And for the RHS:
$(P \cap Q) \cup R = R \cup (P \cap Q)$ ....as operations on sets is commutative
$\Rightarrow (R \cup P) \cap Q = (R \cup P) \cap (R \cup Q)$
Thus, $P \cap (Q \cup R) \neq (P \cap Q) \cup R$

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