Is it true that for any sets A and B, P (A) ...

NCERT Class XI Mathematics - Sets - Solutions

Question : 64 of 73

Marks: +1, -0

Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer.

Solution:

No, it is not true.

Take A = {1, 2} and B = {2, 3}

Then A ∪ B = {1, 2, 3}

⇒ P(A) = {f, {1}, {2}, {1, 2}} and

P(B) = {f, {2}, {3}, {2, 3}}

∴ P(A) ∪ P(B) = {f, {1}, {2}, {3}, {1, 2}, {2, 3}} .....(i)

A ∪ B = {1, 2, 3}

⇒ P(A ∪ B) = {f, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}} .....(ii)

From (i) and (ii), we have

P(A ∪ B) ≠ P(A) ∪ P(B).

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