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Question
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.
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Solution
A = [1, 2, 3,..., 14]
R = {(x, y) : 3x − y = 0, where x, y ∈ A}
Or,
R = {(x, y) : 3x = y, where x, y ∈ 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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