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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions2 Marks
Question
Determine whether the below relation is reflexive, symmetric and transitive:
Relation R in the set A of human beings in a town at a particular time given by
R = {(x, y) : x and y work at the same place}
✓

Answer

It is given that R = {(x, y) : x and y work at the same place}
Clearly, (x, x) $\in$ R, as we can say x and x work at the same place.
$\Rightarrow$ R is reflexive.
Now, if (x, y) $\in$ R, then x and y work on the same place.
$\Rightarrow$ y and x work at the same place.
$\Rightarrow$ (y, x) $\in$ R
$\Rightarrow$ R is symmetric.
Further, let (x, y), (y, z) $\in$ R
$\Rightarrow$ x and y work at the same place and y and z work at the same place.
$\Rightarrow$ x and z work at the same place
$\Rightarrow$ (x, z) $\in$ R
$\Rightarrow$ R is transitive.
Therefore, R is reflexive, symmetric and transitive.

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