Relation on A Defined by 3x − y = 0 | Domain, Co-domain and Range

Relation on \(A\) Defined by \(3x-y=0\)

Question

Let \[ A=\{1,2,3,\ldots,14\} \]

Define a relation on \(A\) by

\[ R=\{(x,y):3x-y=0,\ x,y\in A\} \]

Depict this relation using an arrow diagram. Write its domain, co-domain and range.

Given,

\[ 3x-y=0 \]

\[ y=3x \]

Possible ordered pairs in \(A\):

\[ (1,3),(2,6),(3,9),(4,12) \]

Therefore,

\[ R=\{(1,3),(2,6),(3,9),(4,12)\} \]

1 → 3
2 → 6
3 → 9
4 → 12

Domain:

\[ \boxed{ \{1,2,3,4\} } \]

Co-domain:

\[ \boxed{ \{1,2,3,\ldots,14\} } \]

Range:

\[ \boxed{ \{3,6,9,12\} } \]

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