Q. 84.2( 13 Votes )

Given a non-empty set X, consider P(X) which is the set of all subsets of X.

Define the relation R in P(X) as follows:

For subsets A, B in P(X), ARB if and only if A B. Is R an equivalence relation on P(X)? Justify your answer.

Answer :

We know that every set is a subset of itself, ARA for all A ϵ P(X).

R is reflexive.


This cannot be implied to B A.


So, if A = {1, 2} and B = {1, 2, 3}, then it cannot be implied that B is related to A.


R is not symmetric.


So, if ARB and BRC, then A B and B C.


A C


R is transitive.


Therefore, R is not an equivalence relation since it is not symmetric.


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