Question

Is it true that for any sets A and B, 

P (A) ∪ P (B) = P (A ∪ B)? 

Justify your answer. 

Answer 1

False 

Let   A = {0, 1} and B = {1, 2}  7 

∴ A ∪ B = {0, 1, 2} 

P(A) = {Φ, {0}, {1},{0, 1}}

P(B) = {Φ, {1}, {2}, {1, 2}}

 P(A ∪ B) = {Φ, {0}, {1}, {2}, {0, 1}, {1, 2}, {0, 2}, {0, 1, 2}} 

P(A) ∪ P(B) = {Φ, {0}, {1}, {0, 1}, {2}, {1, 2}} 

∴ P(A) ∪ P(B) ≠ P(A ∪ B)