(1) and (2) are both satisfied. So what about (3)? because and because . But ?Let be subsets of . Explain why the relation ~ on S defined by x~y if and only if for some is NOT an equivalence relation on S.
I know that in order ~ to be an equivalence relation, ~ must be:
1) (reflexive) x~ x for all x in X.
2) (symmetric) If x~ y then y~ x.
3) (transitive) If x~ y and y~ z, then x~ z.
But, I just can't find a counter example for which it doesn't satisfy one or more of 1,2,3.