55. Is it true that for any sets A and B, P (A) <math><mrow><mo>∪</mo></mrow></math> P(B) = P (A <math><mrow><mo>∪</mo></mrow></math> B) ? Justify your answer.

55. Let A = {a}, B = {b}.So, P (A) = {? , {a}}B (A)= {? , (b}}So, P (A) ∪P {B} = {? , {a}, {b}} ______ (1)Now, A∪B = {a, b}.P (A∪B) = {? , {a}, {b}, {a, b}} ____ (2)So. From (1) and (2) we see that, P (A)∪ P (B) ≠P (A∪B)

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

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Payal Gupta | Contributor-Level 10

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55. Let A = {a}, B = {b}.

So, P (A) = ${?, {a}} B (A) = {?, (b}}$

So, P (A) $\cup$ P {B} = ${?, {a}, {b}}$ ______ (1)

Now, A $\cup$ B = {a, b}.

P (A $\cup$ B) = ${?, {a}, {b}, {a, b}}$ ____ (2)

So. From (1) and (2) we see that,

P (A) $\cup$ P (B) ≠P (A $\cup$ B)

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

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