If R is a relation from A = {1,2, 3, 4} to B = {1, 3, 5} such that (a, b) ∈R ↔     a < b, then R o R–1 is {(3, 3), (3, 5), (5, 3), (5, 5)}.Group startsTrue or FalseTrue, unselectedFalse, unselected

To determine if the statement is true or false, we need to find the composition of R with its inverse, R^-1.

First, let's find R^-1. The inverse of R is obtained by swapping the elements in each ordered pair. So, R^-1 = {(b, a) | (a, b) ∈ R}.

Given that R = {(a, b) | a < b}, we can find R^-1 by swapping the elements in each ordered pair. Thus, R^-1 = {(b, a) | b < a}.

Now, let's find the composition of R with R^-1, denoted as R o R^-1. The composition is obtained by taking the ordered pairs from R and R^-1 and combining them in such a way that the second element of the pair from R matches the first element of the pair from R^-1.

In this case, R o R^-1 = {(a, c) | (a, b) ∈ R and (b, c) ∈ R^-1}.

Let's go through the ordered pairs in R and R^-1 to find the pairs that satisfy the condition.

For (1, 3) ∈ R, there is no pair in R^-1 that has 3 as the first element. For (1, 5) ∈ R, there is no pair in R^-1 that has 5 as the first element. For (2, 3) ∈ R, there is no pair in R^-1 that has 3 as the first element. For (2, 5) ∈ R, there is no pair in R^-1 that has 5 as the first element. For (3, 5) ∈ R, there is a pair in R^-1 that has 5 as the first element, which is (5, 3). For (4, 5) ∈ R, there is no pair in R^-1 that has 5 as the first element.

Therefore, the composition R o R^-1 is {(3, 3), (3, 5), (5, 3), (5, 5)}.

Hence, the statement is true.