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Relations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations2 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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