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

  1. Chapter 1 Class 11 Sets
  2. Serial order wise
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Misc 6, Assume that P (A) = P (B). Show that A = B. Inorder 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 Similarly, We can prove B ⊂ A Now since A ⊂ B & B ⊂ A ∴ A = B Hence proved

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