NCERT Class XI Mathematics - Sets - Solutions
© examsnet.com
Question : 63
Total: 73
Assume that P(A) = P(B). Show that A = B
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.
⇒ 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.
© examsnet.com
Go to Question: