In a certain town,25% of the families own a p | vedclass

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Question

(C) Let $P$ be the set of families owning a phone and $C$ be the set of families owning a car.Given: $n(P) = 25\%$,$n(C) = 15\%$,and $n(P' \cap C') =

Vedclass · Accepted Answer

All $(A), (B)$ and $(C)$ are correct.

Vedclass · Answer

(C) Let $P$ be the set of families owning a phone and $C$ be the set of families owning a car.Given: $n(P) = 25\%$,$n(C) = 15\%$,and $n(P' \cap C') = 65\%$.Using De Morgan's Law,$n(P \cup C) = 100\% - n(P' \cap C') = 100\% - 65\% = 35\%$.Thus,statement $(B)$ is correct.Now,$n(P \cap C) = n(P) + n(C) - n(P \cup C) = 25\% + 15\% - 35\% = 5\%$.Thus,statement $(A)$ is correct.Given that $5\%$ of the total families $x$ is $2,000$,we have $0.05x = 2,000$.$x = \frac{2,000}{0.05} = 40,000$.Thus,statement $(C)$ is correct.Therefore,all statements $(A), (B),$ and $(C)$ are correct.

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