1. The problem statement, all variables and given/known data On the set of integers, define the relation R by: aRb if ab>=0. Is R an equivalence relation? 2. Relevant equations 3. The attempt at a solution R is an equivalence relation if it satisfies: 1) R is reflexive Show that for all a∈Z, aRa. Let a∈Z. Then if a is a negative integer, aa>=0. If a is a positive integer, aa>=0. And if a = 0, aa>=0. Hence aRa I feel like it is too simple.. lacking something?? 2) R is symmetric Show that for all a∈Z, aRb --> bRa Let a∈Z, b∈Z such that aRb. By the definition of R, ab>=0. This is not symmetric. Take a = -1, b = 2. Then we have ab = -2 which is not >= 0. 3) R is transitive if aRb and bRc implies aRc for all a,b,c ∈ Z Let a, b, c ∈ Z s/t aRb, bRc --> aRc Now I think this one is true.. but I'm not sure. But since aRb, and bRc, then you would always have ab or bc >=0 yea? so that means aRc must be true.. How would I prove it properly if it is correct? Any help is appreciated! :) Thanks.