Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8}

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}

 

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