Question

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

Answer 1

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 $\left(a,b\right)\in R\iff a^2+b^2=25$
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).