If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R? ans. {(1, 1), (2, 1), (4, 3), (3, 1)} {(1, 1), (3, 1), (2, 3), (4, 2)} 1{(1, 3), (3, 3), (3, 4), (3, 2)} f{(1, 1), (9, 1), (4, 9), (16, 4)}

The composite of a relation R with itself, denoted as R2, is defined as follows: for any (a, b) and (c, d) in R, if b = c, then (a, d) is in R2.

Let's calculate R2 for R = ((1, 1), (3, 1), (2, 3), (4, 2)):

1. Start with the first pair in R: (1, 1). The second element is 1. Look for other pairs in R where the first element is also 1. We find (1, 1). So, (1, 1) is in R2.

2. Next, consider the pair (3, 1). The second element is 1. Look for other pairs in R where the first element is also 1. We find (1, 1). So, (3, 1) is in R2.

3. Now, consider the pair (2, 3). The second element is 3. Look for other pairs in R where the first element is also 3. We find none. So, there are no pairs in R2 from (2, 3).

4. Finally, consider the pair (4, 2). The second element is 2. Look for other pairs in R where the first element is also 2. We find (2, 3). So, (4, 3) is in R2.

Therefore, R2 = {(1, 1), (3, 1), (4, 3)}.

So, the correct answer is the first option: {(1, 1), (3, 1), (4, 3)}.