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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions3 Marks
Question
Determine whether the below relation is reflexive, symmetric and transitive:
Relation R in the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y) : y is divisible by x}
✓

Answer

It is given that relation R on the set A = {1, 2, 3, 4, 5, 6} as
R = {(x, y) : y is divisible by x}
We know that any number 'x' is divisible by itself.
$\Rightarrow$ (x, x) $\in$ R $\forall$ $x\in A$
$\Rightarrow$ R is reflexive.
Now, (2, 4) $\in$ R but (4, 2) $\notin$ R.
$\Rightarrow$ R is not symmetric.
Let (x,y), (y,z) $\in$ R.
$\Rightarrow$y is divisible by x and z is divisible by y.
$\Rightarrow$ z is divisible by x.
$\Rightarrow$ (x,z) $\in$ R
$\Rightarrow$ R is transitive.
Therefore, R is reflexive and transitive but not symmetric.

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