If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R?

To find the composite relation R2 = R o R, we need to find all pairs (a, c) such that there exists a b for which (a, b) and (b, c) are in R.

The given relation R is: R = {(1, 1), (3, 1), (2, 3), (4, 2)}

Let's find R2 step by step:

1. Start with the first pair in R, (1, 1). We are looking for a pair in R that starts with 1 (the second element of our starting pair). We have two such pairs: (1, 1) and (1, 1). So, from the pair (1, 1), we get two pairs in R2: (1, 1) and (1, 1).

2. Take the second pair in R, (3, 1). We are looking for a pair in R that starts with 1. We have two such pairs: (1, 1) and (1, 1). So, from the pair (3, 1), we get two pairs in R2: (3, 1) and (3, 1).

3. Take the third pair in R, (2, 3). We are looking for a pair in R that starts with 3. But there is no such pair. So, we don't get any pair in R2 from (2, 3).

4. Take the fourth pair in R, (4, 2). We are looking for a pair in R that starts with 2. We have one such pair: (2, 3). So, from the pair (4, 2), we get one pair in R2: (4, 3).

So, the composite relation R2 = R o R is: R2 = {(1, 1), (1, 1), (3, 1), (3, 1), (4, 3)}