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Question
If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.
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Solution
Given:
R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4}
We know:
\[\left( - 2 \right)^2 + 0^2 \leq 4\]
\[ \left( 2 \right)^2 + 0^2 \leq 4\]
\[ \left( - 1 \right)^2 + 0^2 \leq 4\]
\[ \left( 1 \right)^2 + 0^2 \leq 4\]
\[ \left( - 1 \right)^2 + \left( 1 \right)^2 \leq 4\]
\[ 0^2 + 0^2 \leq 4\]
\[ \left( 1 \right)^2 + \left( 1 \right)^2 \leq 4\]
\[ \left( - 1 \right)^2 + \left( - 1 \right)^2 \leq 4\]
∴ Domain (R) = {-2,-1, 0, 1, 2}
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