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Question
If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation on Z, then the domain of R is ______.
Options
{0, 1, 2}
{0, −1, −2}
{−2, −1, 0, 1, 2}
{−1, 0, 1}
None of these
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Solution
If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation on Z, then the domain of R is {−2, −1, 0, 1, 2}.
Explanation:
R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4}
We know that,
\[\Rightarrow \left( - 2 \right)^2 + 0^2 \leq 4\]
\[ \Rightarrow \left( 2 \right)^2 + 0^2 \leq 4\]
\[ \Rightarrow \left( - 1 \right)^2 + 0^2 \leq 4\]
\[ \Rightarrow \left( 1 \right)^2 + 0^2 \leq 4\]
\[ \Rightarrow \left( - 1 \right)^2 + \left( 1 \right)^2 \leq 4\]
\[ \Rightarrow 0^2 + 0^2 \leq 4\]
\[ \Rightarrow \left( 1 \right)^2 + \left( 1 \right)^2 \leq 4\]
\[ \Rightarrow \left( - 1 \right)^2 + \left( - 1 \right)^2 \leq 4\]
Hence, domain (R) = {−2, −1, 0, 1, 2}.
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