Let A 123 and B 345 and R be a relation from A to B descri

Let A = {1,2,3} and B = {3,4,5} and R be a relation from A to B described as follows:

a R b if and only if a | b (a divides b)

List the elements of AxB, R, and the inverse of R.

Solution

Given A = {1, 2, 3}. B = {3, 4, 5}.

AxB = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5)}.

R = a R b if and only if, a | b.

So, R = {(1, 3), (1, 4), (1, 5), (2, 4), (3, 3)}.

Inverse of R: {(3, 1), (4, 1), (5, 1), (4, 2), (3, 3)}.