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 ______ .
Solution:
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 $R$.