Let $R$ be a reflexive relation on a finite set $A$ containing $n$ elements,and let $R$ contain $m$ ordered pairs. Then,

Let $M$ denote the set of all $3 \times 3$ non-singular matrices. Define the relation $R$ by $R = \{ (A,B) \in M \times M : AB = BA \}$. Then $R$ 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 $R = \{(x, y): x \text{ and } y \text{ work at the same place}\}$.

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

$A$ relation $R$ defined on a set $A$ is anti-symmetric if $(a, b) \in R$ and $(b, a) \in R$ implies:

Let $L$ be the set of all straight lines in a plane and the relation $R$ on $L$ is defined by $\alpha R \beta \Leftrightarrow \alpha \perp \beta$,where $\alpha, \beta \in L$. Then $R$ is: