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.

Answer: 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) }.