Question

12. Assume that P(A) = P(B).
Show that A=B.​

Answer 1

Answer:

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Step-by-step explanation:

P(A)=P(B)

inorder to prove A=B, we should prove A is a subset of B i.e., A⊂B

and B is a subset of A i.e., B⊂A

Set A is an element of power et of A as every set is a subset

i.e., P∈P(A)

A∈P(B)

if set A is in power set of B

Set A is a subset of B

A⊂B

Similarly we can prove

B⊂A

Now since A⊂B and B⊂A

∴ A=B

Hence proved