Let A= {1, 2, 3,….,14}. Define a relation on a set A by R= {(x, y): 3x – y = 0, where x, y A}. Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.
Given, R= {(x, y): 3x – y = 0, where x, y A}
A= {1, 2, 3,…,14}
As, y = 3x
∴ R= {(x, 3x): where x, 3x A}
⇒ R= {(1, 3×1), (2, 3×2), (3, 3×3), (4, 3×4)}
NOTE: We cannot include (5, 3×5) as 15 ∉ A
⇒ R = {(1, 3), (2, 6), (3, 9), (4, 12)}
So,
Domain of relation R= {1, 2, 3, 4}
Co-Domain of relation R= {1, 2, 3,…,14}= A
Range of relation R= {3, 6, 9, 12}