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Relation — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRelation2 Marks
Question
Let R be a relation in N defined by $\text{x, y}\in\text{R}\Leftrightarrow\text{x}+2\text{y}=8.$ Express $R$ and $R^{−1}$ as sets of ordered pairs.
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Answer

We have, $\text{x, y}\in\text{R}\Leftrightarrow\text{x}+2\text{y}=8$ Now, $x + 2y = 8$
$\Rightarrow x = 8 - 2y$ Putting y = 1, 2, 3, we get x = 6, 4, 2 respectively. For y = 4, we get $\text{x}=0\notin\text{N}$ Also, for y > 4, $\text{x}\notin\text{N}$
$\therefore$ R = {(6, 1), (4, 2), (2, 3)} Thus, $R^{-1} = {(1, 6), (2, 4), (3, 2)}$
$\Rightarrow R^{-1} = {(3, 2), (2, 4), (1, 6)}$

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