Let A = [1, 2, 3, ……., 14]. Define a relation on a set A by
Question:

Let A = [1, 2, 3, ……., 14]. Define a relation on a set A by

R = {(xy) : 3x − y = 0, where xy ∈ A}.

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

Solution:

A = [1, 2, 3,…, 14]

R = {(xy) : 3x − y = 0, where xy ∈ A}

Or,

R = {(xy) : 3x = y, where xy ∈ A}

As

$3 \times 1=3$

 

$3 \times 2=6$

$3 \times 3=9$

 

$3 \times 4=12$

Or,

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



Domain (R) = {1, 2, 3, 4}

Range (R) = {3, 6, 9, 12}

Co-domain (R) = A

 

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