 Questions & Answers    Question Answers

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

Bookmark added to your notes.
View Notes
Domain and Range Relations  Speech on Vocational Education is The Need of The Hour  On the Face of It - Summary  Speech on The Internet  The Language of Mathematics  Speech on Indian Army in Upholding The Security of The Nation  Domain and Range of a Function  Impact of Human Activities on the Hydrosphere  Indian Economy on The Eve of Independence  Agriculture Sector on the Eve of Independence  