Let R be the relation on integers defined by aRb if and only if 2a+3b congruent to 0 (mod 5). Show that this is an equivalence relation.
ok, symmetry is a bit difficult, i'l admit when seeing this for the first time. so i will do it for you. but i will leave transitivity to you. just express the congruence as i did.
Note that means for some
Claim: R is symmetric
Proof: Assume , that is, for some integer
Then,
since , we have
Thus, R is symmetric