Question

If A = {3, 5, 6, 9) and R is a relation in A defined as R = {(x, y) : x + y < 18), then R in roster form is ______ .

Answer 1

A = {3, 5, 6, 9)
R = {(x, y) : x + y < 18 }
Then roaster form for R is collection of elements of type {(x, y)} satisfying R.
for x = 3, possible values of y are 3, 5, 6, 9
for x = 5, possible values of y are 3, 5, 6, 9
for x = 6, possible values of y are 3, 5, 6, 9
for x = 9, possible values of y are 3, 5, 6.

$\therefore$ R = { (3, 3) (3, 5) (3, 6) (3, 9) (5, 3) (5, 5) (5, 6) (5, 9) (6, 3) (6, 5) (6, 6) (6, 9) (9, 3) (9, 5) (9, 6)} is the roaster form for R.