Question

For any sets A and B, show that
P(A intersectionB ) = P(A) intersection P(B).​

Answer 1

Answer:

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.

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