I'm having trouble with these types of problems. Any help would be greatly appreciated .

I know that in order ~ to be an equivalence relation, ~ must be:Let $\displaystyle A_1 = \{0,1\}, A_2 = \{1,2\}, A_3 = \{3,4\} $ be subsets of $\displaystyle S = \{0,1,2,3,4\}$. Explain why the relation ~ on S defined by x~y if and only if $\displaystyle x,y \in A_i $ for some $\displaystyle i \in \{1,2,3\}$ isNOTan equivalence relation on S.

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.