Question

R on the set {1,2,3,4,5}, so that (x,y) is in R if 3 divides x+y. List the elements of R.

Answer 1

Answer:  The elements of R are

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

Step-by-step explanation:  We are given a relation R on the set {1, 2, 3, 4, 5} so that (x, y) is in R if 3 divides x+y.

We are to list the elements of R.

We see that

if x = 1 and y = 2, 5, then x + y = 3 and 6 so that 3 divides x+y.

If x = 2 and y = 1, 4, then x + y = 3 and 6 so that 3 divides x+y.

If x = 3 and y = 3, the x + y = 6 so that 3 divides x+y.

If x = 4 and y = 2, 5, then x + y = 6 and 9 so that 3 divides x+y.

If x = 5 and y = 1, 4, then x + y = 6 and 9 so that 3 divides x+y.

Therefore, the elements in R are listed as follows :

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

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