Question:
Let $A=\{0,1,2,3,4,5,6,7,8\}$ and let $R=\{(a, b): a, b \in A$ and $2 a+3 b=12\}$.
Express R as a set of ordered pairs. Show that R is a binary relation on A. Find its domain and range.
Solution:
$A=\{0,1,2,3,4,5,6,7,8\}$
2a + 3b = 12
$b=\frac{12-2 a}{3}$
$a=0$ è $b=4$
$a=3$ è $b=2$
$a=6$ è $b=0$
$R=\{(0,4),(3,2),(6,0)\}$
Since, R is a subset of A × A, it a relation to A
The domain of R is the set of first co-ordinates of R
Dom(R) = {0, 3, 6}
The range of R is the set of second co-ordinates of R
Range(R) = {4, 2, 0}