Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSETS2 Marks
Question
Assume that P(A) = P(B) show that A = B.
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Answer
Let$X \in A \Rightarrow \{ x\} \in P(A)$ $\Rightarrow \{ x\} \in P(B)\,[\because P(A) = P(B)]$ $\Rightarrow X \notin B$ $\therefore A \subset B$. . . (i) Let $X \in B \Rightarrow \{ x\} \in P(B)$ $\Rightarrow \{ X\} \in P(A)\,[\because \,P(A) = P(B)]$ $ \Rightarrow X \in A$. . . (ii) $\therefore B \subset A$ From (i) and (ii) we have A = B
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