Write the domain of the relation R defined on the set Z of integers as follows: $\left( {a,b} \right) \in R \Leftrightarrow {a^2} + {b^2} = 25$

Hint- Here, we will find out all the possible cases corresponding to the values satisfying the given relation.

The given relation defined on Z is $\left( {a,b} \right) \in R \Leftrightarrow {a^2} + {b^2} = 25$
Since both $a$ and $b$ belongs to the set of integers that means they can only have integer values.
Now, the various set of integers $\left( {a,b} \right)$ possible for ${a^2} + {b^2} = 25$ to be satisfied are $\left( { \pm 5,0} \right)$, $\left( { \pm 4, \pm 3} \right)$, $\left( { \pm 3, \pm 4} \right)$ and \[\left( {0, \pm 5} \right)\].
Therefore, the domain of the given relation is the possible values of $a$ and $b$ which is $\left\{ {0, \pm 3, \pm 4, \pm 5} \right\}$.

Note- Domains of a relation or function are all the values that can go in a relation or function (input) and range of a relation or function are all the values that the relation or function can show (output).