Question
Let A = {1, 2, 3, ......., 14}. Define a relation on a set A by $\text{R}=\text{(x, y)} : 3\text{x}= 0, \text{where x, y} ∈ \text{A}$ Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.
✓
Answer
We have, 3x - y = 0 ⇒ 3x = y ⇒ y = 3x Putting x = 1, 2, 3, 4 we get y = 3, 6, 9, 12 respectively. For x > 4, we get y > 14 which does not belong to set A. $\therefore$ R = {(1, 3), (2, 6), (3, 9), (4, 12)} The arrow diagram representing R is as follows: Clearly, Domain(R) = {1, 2, 3, 4} Co-domain(R) = {1, 2, 3, 4, ....., 14} and Range(R) = {3, 6, 9, 12}
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