Question

Can you conclude that a = b if a and b are two sets with the same power set?

Answer 1

The sets A and sets B contains items called elements

It is true that the set A is equal to set B

How to determine the true statement?

The sets are given as:

Set A and set B

Since the sets have the same power set, then we have:

P(A) = P(B)

The above means that:

For every element X in A, then the element is also in B

And

For every element Y not in A, then the element is also not in B

So, we can conclude that:

All subsets of the set A are subsets of the set B and vice versa

Hence, the set A is equal to set B

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