Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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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. - Mathematics

If R = {(xy) : xy ∈ 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 = {(xy) : xy ∈ 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}

Concept: Relation
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Q 4 | Page 25
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