Suppose a = {1, 2, 3, 4}. let s and r be relations on a defined as follows:
s = { (1, 1), (1, 3), (2, 3), (3, 4), (4,1) }
r = { (1, 4), (2, 2), (3, 2), (4, 2) }
write down the set of pairs in s ο r.

 The required set of pairs is {(1, 1), (2, 3), (3, 3), (4, 3)}.

Step-by-step explanation:  We are the set A = {1, 2, 3, 4} and S, R are relations on A , defined as follows :

S = {(1, 1), (1, 3), (2, 3), (3, 4), (4,1)}

R = {(1, 4), (2, 2), (3, 2), (4, 2)}.

We are to write the set of pairs in   S ο R.

We know that for any element x in R, we get

S ο R(x) = S(R(x)).

From the given relations, we have

S ο R(1) = S(R(1)) = S(4) = 1, so the pair is (1, 1).

S ο R(2) = S(R(2)) = S(2) = 3, so the pair is (2, 3).

S ο R(3) = S(R(3)) = S(2) = 3, so the pair is (3, 3).

S ο R(4) = S(R(4)) = S(2) = 3, so the pair is (4, 3).

Thus, the required set of pairs is {(1, 1), (2, 3), (3, 3), (4, 3)}.

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