If A = {3, 5, 6, 9) and R is a relation in A defined as R

Question:

If A = {3, 5, 6, 9) and R is a relation in A defined as R = {(xy) : 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 {(xy)} 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 $R$.

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