Let $R$ be a relation on a set $A$ such that $R = R^{-1}$. Then $R$ is:

Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is:

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, a) \in R$,for all $a \in N$

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $N$ of natural numbers defined as
$R = \{(x, y) : y = x + 5 \text{ and } x < 4\}$

On the set $N$ of natural numbers,the relation $R$ is defined by $nRm$ if $n$ is a factor of $m$ (i.e.,$n|m$). Then $R$ is:

The number of relations on the set $A = \{1, 2, 3\}$ containing at most $6$ elements including $(1, 2)$,which are reflexive and transitive but not symmetric,is . . . . . . .