Let the set A be defined as A a b c d and let the relations

Let the set A be defined as A = {a, b, c, d}, and let the relations R and S on the set A be defined as R = {(d, a), (a, b), (b, c)}, and S = {(a, a), (b, d), (d, c)}. Explain why the ordered pair (a, b) is or is not an element of the composition of S and R (denoted R o S).

Solution

The ordered pair (a,b) is in RoS because (a,a) belongs to S and (a,b) belongs to R implies that (a,b) is an element of RoS.