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Misc 6 - Assume that P(A) = P(B). Show that A = B - Sets Class 11

Misc 6 - Chapter 1 Class 11 Sets - Part 2

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Misc 6 Assume that P (A) = P (B). Show that A = B. In order to prove A = B, we should prove A is a subset of B i.e. A ⊂ B & B is a subset of A i.e. B ⊂ A Set A is an element of power set of A as every set is a subset (Eg: for set A = {0, 1} , P(A) = { ∅ , {0}, {1}, {0, 1} } So, A is in P(A)) i.e. A ∈ P(A) ⇒ A ∈ P(B) If set A is in power set of B, set A is a subset of B ∴ A ⊂ B ⊂ Subset A ⊂ B (All elements of set A in set B) Similarly, We can prove B ⊂ A Now since A ⊂ B & B ⊂ A ∴ A = B Hence proved

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.