If $R$ is a relation on the set $N$, defined by $\left\{ {\left( {x,y} \right);3x + 3y = 10} \right\}$

Statement $-1$ : $R$ is symmetric

Statement $-2$ : $R$ is reflexive

Statement $-3$ : $R$ is transitive, then thecorrect sequence of given statements is

(where $T$ means true and $F$ means false)

Show that the relation $R$ defined in the set $A$ of all polygons as $R=\left\{\left(P_{1}, P_{2}\right):\right.$ $P _{1}$ and $P _{2}$ have same number of sides $\}$, is an equivalence relation. What is the set of all elements in $A$ related to the right angle triangle $T$ with sides $3,\,4$ and $5 ?$

Determine whether each of the following relations are 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 $y$ live in the same locality $\}$

If $R$ is a relation from a set $A$ to a set $B$ and $S$ is a relation from $B$ to a set $C$, then the relation $SoR$

Let $S$ be the set of all real numbers. Then the relation $R = \{(a, b) : 1 + ab > 0\}$ on $S$ is

$R$ is a relation over the set of real numbers and it is given by $nm \ge 0$. Then $R$ is