Question

If R = {(x,y) : $\pm 2$} is a relation in Z, then domain of R is
A. {0,1,2}
B. {-2,-1,0}
C. {-2,-1,0,1,2}
D. None of these

Answer 1

Hint: We are given a function and we have to find the domain of that function. The domain of a function is that the set of values that we have a tendency to square measure is allowed to plug into our function. This set is the x values in a function like f(x). Now to solve this question, we put x equal to 0, $\pm 1$, $\pm 2$ and find out the values of y. By combining the y values, we get the domain of R.

Complete step by step solution:
We are given that $\{(x,y) : x,y\in Z,{{x}^{2}}+{{y}^{2}}\le 4\}$ is a relation in Z.
We have to find the domain of R.
First we suppose that x = 0
We know ${{x}^{2}}+{{y}^{2}}\le 4$
That is ${{y}^{2}}\le 4$
By solving the above equation we get y = 0, $\pm 1,\pm 2$
Similarly, we suppose that x = $\pm 1$
As ${{x}^{2}}+{{y}^{2}}\le 4$
That is ${{y}^{2}}\le 3$
By solving the above equation, we get y = 0, $\pm 1$
Now we suppose that x = $\pm 2$
As ${{x}^{2}}+{{y}^{2}}\le 4$
That is ${{y}^{2}}\le 0$
By solving the above equation, we get y = 0
Therefore, R = {(0,0), (0,-1), (0,-2), (0,2), (-1,0), (1,0), (1,1), (1,-1), (-1,1), (2,0), (-2,0)}
Hence, domain of R = (x : (x,y) $\in R$} = {0,-1,1,-2,2}

Option ‘C’ is correct

Note: While solving this type of question you need to know that all of the values that can go into a relation or function (input) are called the domain and the values that come out of a relation or function (output) are called the range.