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Misc 7 - Is it true that P(A) U P (B) = P (A U B) - Sets - Proof - where properties of sets cant be applied,using element

  1. Chapter 1 Class 11 Sets
  2. Serial order wise
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Misc 7 Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer. (We take an example to see if it is false, 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 is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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