In a plane,two points $P$ and $Q$ are related if $OP = OQ$,where $O$ is a fixed point. The relation is:

$A$ relation $R$ defined on the set $A = \{a, b, c\}$ is given by $R = \{(a, a), (b, b), (c, c), (a, c)\}$. This relation is . . . . . . .

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $A$ of human beings in a town at a particular time given by:
$R = \{(x, y) : x \text{ is exactly } 7 \, cm \text{ taller than } y\}$

Let $R = \{ (3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6) \}$ be a relation on the set $A = \{ 3, 6, 9, 12 \}$. The relation is

Let $R$ be a relation on the set $A$ of ordered pairs of positive integers defined by $(x, y) R (u, v)$ if and only if $xv = yu$. Show that $R$ is an equivalence relation.

Let $A$ be the non-void set of the children in a family. The relation '$x$ is a brother of $y$' on $A$ is