Question:
Let A = {2, 3, 5} and R = {(2, 3), (2, 5), (3, 3), (3, 5)}. Show that R is a binary relation on A. Find its domain and range.
Solution:
First, calculate A×A.
A×A = {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)}
Since, $R$ is a subset of $A \times A$, it's a binary relation on $A$.
The domain of $R$ is the set of first co-ordinates of $R$
Dom(R) = {2, 3}
The range of R is the set of second co-ordinates of R
Range(R) = {3, 5}