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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Can you conclude that a = b if a and b are two sets with the same power set?
Solution:
Given a and b are two sets with the same power set,
⇒ P(A) = P(B)
Now, let X ⊂ A
Then X ∈ P(A)
⇒ X ∈ P(B) [ ∵P(A) = P(B)]
⇒ X ⊂ B
Similarly, ∀ Y ⊂ B, we can prove that Y ⊂ A.
Thus, every subset of A is a subset of B and every subset of B is a subset of A.
∴ A = B
Can you conclude that a = b if a and b are two sets with the same power set?
Summary:
If A and B are two sets with the same power set, A = B.
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