Question

For any sets A and B prove that

(a) P(A∩B) =P(A) ∩ P(B)​

Answer 1

Step-by-step explanation:

We have to show that P(A ∩ B) = P(A) ∩ P(B)

LHS:

Let x ∈ P(A ∩ B)

=> x ∈ (A ∩ B)

=> x ∈ A and x ∈ B .............1

RHS:

x ∈ P(A) ∩ P(B)

=> x ∈ A and x ∈ B ............2

From equation 1 and 2, we get

P(A ∩ B) = P(A) ∩ P(B)

Hence proved.