Misc 7 - Is it true that P(A) U P (B) = P (A U B) - Sets

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Question 2 Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer. (If it is false, we take an example to prove it) Let A = {0, 1} and B = {1, 2} ∴ A ∪ B = {0, 1, 2} P(A ∪ B) = {∅, {0}, {1}, {2}, {0, 1}, {1, 2}, {0, 2}, {0, 1, 2} } ∴ P(A) ∪ P(B) ≠ P(A ∪ B) So, the given statement is False P(A) = {∅ , {0}, {1}, {0, 1}} P(B) = {∅, {1}, {2}, {1, 2}} P(A) ∪ P(B) = {∅, {0}, {1}, {0, 1}, {2}, {1, 2}}

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.