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

NCERT Class XI Mathematics - Sets - Solutions

Question : 63 of 73

Marks: +1, -0

Solution:

Let x ∈ A ⇒ {x} ∈ P(A) ⇒ {x} ∈ P(B) [Since P(A) = P(B)]

⇒ x ∈ B ∴ A ⊂ B .....(i)

Let x ∈ B ⇒ {x} ∈ P(B) ⇒ {x} ∈ P(A) [Since P(A) = P(B)]

⇒ x ∈ A ∴ B ⊂ A .....(ii)

From (i) and (ii), we have A = B.

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