Explanation:
S°R can be seen as exercising the relation R first, and then using the result of R to exercise the relation S.
the x values of R therefore drive the composition :
1, 2, 3
let's start with x = 1.
when x = 1, then R gives us the possible y values of 2 and 3.
that means we can go with x = 2 and x = 3 into S.
x = 2 gives us y = 1 in S.
x = 3 gives us y = 1 or 2 in S.
therefore S°R(x = 1) = {(1, 1), (1, 2)}
when x = 2, then R gives us the possible y values of 3 and 4.
that means we can go with x = 3 and x = 4 into S.
x = 4 gives us y = 2 in S.
x = 3 gives us y = 1 or 2 in S.
S°R(x = 2) = {(2, 1), (2, 2)}
when x = 3, then R gives us the possible y value of 1.
that means we can go with x = 1 into S.
x = 1 gives us y = nothing in S.
S°R(x = 3) = {}
S°R in general is then the union of all 3 sets :
{(1, 1), (1, 2), (2, 1), (2, 2)}