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Equivalence relation on power set P(U) using bijections between subsets

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ahmedmodassir

This document defines an equivalence relation ~ on the power set P(U) of a nonempty set U. Relation A ~ B means there exists a bijection f between subsets A and B of P(U). The solution is to prove that the relation ~ is reflexive, symmetric and transitive, making it an equivalence relation on P(U).

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12. Let U be a nonempty set and let P(U) be the power set of U. That is, P (U) is the set of all subsets of U. For A and B in P(U), define A ~ B to mean that there exists a bijection f : A B. Prove that ~ is an equivalence relation on P(U). Solution U IS A NON EMPTY SET & P[U] IS THE POWER SET OF U A & B ARE ELEMENTS OF P[U] A R B

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Equivalence relation on power set P(U) using bijections between subsets

  • 1. 12. Let U be a nonempty set and let P(U) be the power set of U. That is, P (U) is the set of all subsets of U. For A and B in P(U), define A ~ B to mean that there exists a bijection f : A B. Prove that ~ is an equivalence relation on P(U). Solution U IS A NON EMPTY SET & P[U] IS THE POWER SET OF U A & B ARE ELEMENTS OF P[U] A R B