First slide

Relations XII

Question

Let A be the non-empty set of children in a family. The relation ‘x is a brother of y’ on A is

Easy

A

reflexive
B

symmetric
C

transitive
D

an equivalence relation

Solution

Let r denotes the relation ‘x is brother of x’. Let x $\in$ A. If x is a girl, then we cannot say x is brother of x.
$∴$ (x, x) $\notin$ R
$∴$ R is not reflective
Let (x, y) $\in$ R
$∴$ x is a brother of y.
$∴$ y may or may not be a boy.
$∴$ We cannot say that (y, x) .
$∴$ R is not symmetric
Let (x, y) $\in$ R and (y, z) $\in$ R
$∴$ x is brother of y and y is brother of z.
$∴$ x is brother of z $\Rightarrow$ (x, z) $\in$ R
$∴$ R is transitive

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