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So in order to approach this proof, can I just use the Reflexive, Symmetrical, and Transitive properties that is basically the definition of equivalence relations?

eg. suppose x, y, z are sets contained in S...

Reflexive: x~x <same as> xRx

Symmetry: x~y => y~x <same as> xRy => yRx

Transitive: x~y, y~z => x~z

This seems too elementary, but I just want to make sure.