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), (3, 1), (2, 3), (4, 2)}1{(1, 3), (3, 3), (3, 4), (3, 2)}{(1, 1), (2, 1), (4, 3), (3, 1)}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 three elements a, b, and c, if (a, b) is in R and (b, c) is in R, then (a, c) is in R2.

Given R = {(1, 1), (3, 1), (2, 3), (4, 2)}, we can find R2 by looking for pairs that satisfy the above condition.

• For (1, 1), there is no pair in R where 1 is the second element and the first element is not 1, so there are no new pairs for R2 from this pair.
• For (3, 1), the pairs in R where 1 is the second element are (1, 1) and (3, 1). So, we get the pairs (3, 1) and (3, 3) for R2.
• For (2, 3), the pairs in R where 3 is the second element are (2, 3) and (4, 2). So, we get the pairs (2, 3) and (2, 2) for R2.
• For (4, 2), the pairs in R where 2 is the second element are (1, 1) and (3, 1). So, we get the pairs (4, 1) and (4, 3) for R2.

So, R2 = {(3, 1), (3, 3), (2, 3), (2, 2), (4, 1), (4, 3)}.

None of the options provided match this result. There might be a mistake in the question or the options provided.