1.

For any sets A and B, show that: P(A ∩ B), = P(A) ∩ P(B)

Answer»

Let X ∈ P (A ∩ B),then A ⊂ (A ∩ B). 

So, X ⊂ A and X ⊂ B. 

∴ X ∈ P(A) and X ∩ P(B) 

⇒ X ∈ P(A) and P(B) 

Thus, P(A ∩ B) ⊂ P(A) ∩ P(B) ..(i) 

Again, Let Y ∈ P(A) ∩ P(B),then 

Y ∈ P(A) and Y ∈ P(B) 

So, Y ⊂ A and Y ⊂ B. 

∴ Y ⊂ A ∩ B ⇒ Y ∈ P(A ∩ B) 

Then P(A) ∩ P(B) ∈ P(A ∩ B) ..(ii) 

Hence from (i) and (ii), we gets 

P (A ∩ B) = P(A) ∩ P(B)



Discussion

No Comment Found

Related InterviewSolutions