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

Asked by Abhisek | 11 months ago |  83

1 Answer

Solution :-

It is not true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)

Justification:

Let us assume,

A = {0, 1}

And, B = {1, 2}

A ∪ B = {0, 1, 2}

According to the question,

We have,

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}}

Also,

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

P (A) ∪ P (B ≠ P (A ∪ B)

Hence, the given statement is false

Answered by Pragya Singh | 11 months ago

Related Questions

If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

Class 11 Maths Sets View Answer

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Class 11 Maths Sets View Answer