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Tuesday 15 April 2014

Assume that P (A) = P (B). Show that A = B.

Assume that P (A) = P (B). Show that A = B.

Answer
Every set is a member of power set so that, A ∈ P(A)
Given that P (A) = P (B) So that
A ∈ P(B)
A is a element of power set of B so that,
A ⊂ B ... (1)
Similarly we can prove that
B ⊂ A ... (2)
From equation (1) and (2) we get, A = B

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6 comments:

  1. Unknown13 January 2015 at 21:39

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    ReplyDelete
  2. mr_hazarika_jr14 July 2017 at 08:48

    guven, P(a)=P(b)

    Let, (x,y) belongs to a
    <=> (x,y) belongs to P(a)
    <=> (x,y) belongs to P(b)
    <=> (x,y) belongs to b
    hence,
    a is a subset of b and b is a subset of a
    so we can say that a=b
    PLEASE CAN ANYONE CHECK IF IT IS A RIGHT WAY

    ReplyDelete
  3. Gaurav17 May 2018 at 18:06

    Yes it is a right way

    ReplyDelete
  4. Arambh lodhi3 October 2018 at 01:26

    Vvvvvvvvvvvvery thanks sir

    ReplyDelete
  5. Unknown19 July 2019 at 06:16

    Correct.

    ReplyDelete