Question

If P(A)=P(B) then prove that A = B

Answer 1

HEYA USER ✌

HERES YOUR ANSWER FRIEND,


GIVEN : P(A) = P(B)

TO PROVE : A = B

PROOF : P(A) IS POWER SET OF SET A. THEREFORE, SUBSETS OF SET A ARE THE ELEMENTS OF SET A.

GIVEN P(A) = P(B)

==> THIS SHOWS THAT POWER SETS OF A AND B ARE EQUAL.

==> THEREFORE, SUBSETS OF TWO SETS ARE EQUAL AND HENCE, A AND B MUST CONTAIN SAME ELEMENTS.

HENCE, A = B ...............{ PROVED }

HOPE IT HELPS YOU.

#FROM KENDRIYA VIDYALAYA GANESH KHIND PUNE ✌