Question:
Define a relation R from Z to Z, given by
$\mathbf{R}=\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{Z}$ and $(\mathbf{a}-\mathbf{b})$ is an integer.
Find dom (R) and range (R).
Solution:
Given: $R=\{(a, b): a, b \in Z$ and $(a-b)$ is an integer
The condition satisfies for all the values of a and b to be any integer.
So, $R=\{(a, b):$ for all $a, b \in(-\infty, \infty)\}$
$\operatorname{Dom}(R)=\{-\infty, \infty\}$
Range $(R)=\{-\infty, \infty\}$
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