NCERT Solutions
Class 11 Maths
Sets

Ex.Misc.Q.7
Is it true that for any sets A and B, P(A) ∪ P(B) = P (A ∪ B)? Justify your answer.
It is false.
Let A = {0, 1} and B = {1, 2}
Now, 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}}
So, P(A) ∪ P(B) ≠ P (A ∪ B)