"A relation R on a set A is transitive if whenever aRb and bRc then aRc, that is, if whenever (a,b), (b,c) is an element of R then (a,c) is an element of R. Thus R is not transitive if there exist a,b,c is an element of R such that (a,b), (b,c) is an element of R but (a,c) is not an element of R"
My question is if relation doesn't have (a,b) and (b,c) in it, there is no need for (a,c) to be in the relation. Since the definition uses the word whenever, if the (a,b) and (b,c) aren't in the relation is the relation considered transitive?
Since we don't need (a,c) to be in the relation.
