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

Solution:

False

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

Hence,

A υ B = {1, 2, 3}

P (A) = {Φ, {1}, {2}, {1, 2}}

P (B) = {Φ, {2}, {3}, {2, 3}}

Now,

P (A) υ P (B) = {Φ, {1}, {2}, {1, 2}} υ {Φ, {2}, {3}, {2, 3}}

= {Φ, {1}, {2}, {3}, {1, 2}, {2, 3}}

P (A υ B) = {Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 2, 3}}

We can see that

P (A) υ P (B) ≠ P (A υ B)

Therefore, it is not true that for any sets A and B, P (A) υ P (B) = P (A υ B)

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 7

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

Summary:

Two sets are given. We have proved that it is not true that for any sets A and B, P (A) υ P (B) = P (A υ B)