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Question

If R = \{x, y : x, y \epsilon Z, x^2 + y^2 \leq 4\} is a relation defined on the set Z of integers, then write domain of R.

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Solution

We have,

R={x,y:x,yϵZ,x2+y24}

Now,

x2+y24

y24x2

y4x2

Putting x = - 2, -1, 0, 1, 2, we get yϵz.

For other values of x, we get y/ϵz.

Domain (R) = {-2, -1, 0, 1, 2}


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