Question

If R is an equivalence relation in a set A, prove that the inverse relation R-' is also
an equivalence relation in A.
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Answer 1

Answer:

If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive. The inverse relation S of the relation R is S={(x,y) | (y,x) € R}. 1 : For every element x of X, we have (x,x) € S, because its reverse pair (x,x) € R, as R is reflexive.