Question

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

1) Yes
2) No
3) Cannot be determined

Answer 1

Two sets with the same power set must contain the same elements, which means that the sets themselves are equal.

Step-by-step explanation:

The question asks whether, given two sets with the same power set, we can conclude that the sets themselves are equal. The answer is yes. Two sets are considered to be equal if they contain exactly the same elements. The power set of a set is the set of all its subsets, including the empty set and the set itself. If two sets have the same power set, they must have the same subsets, which implies that they must have the same elements. Hence, if sets A and B have the same power set, then A = B.