Question:
for any sets A and B show that : P(A intersection B) = P(A) intersection P(B)
Answer:
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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