Q. 174.8( 8 Votes )

# 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.

Answer :

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}

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