Assume that P(A)=P(B) . Show that A=B. | vedclass

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Question

Let $P(A)=P(B)$

To show: $A=B$

Let $x \in A$

$A \in P(A)=P(B)$

$	herefore x \in C,$ for some $C \in P(B)$

Now, $C \subset B$

$	her

Vedclass · Accepted Answer

Vedclass · Answer

Let $P(A)=P(B)$

To show: $A=B$

Let $x \in A$

$A \in P(A)=P(B)$

$	herefore x \in C,$ for some $C \in P(B)$

Now, $C \subset B$

$	herefore x \in B$

$	herefore A \subset B$

Similarly, $B \subset A$

$	herefore A=B$

Assume that $P(A)=P(B) .$ Show that $A=B$.

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