Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is

Let $R$ be a reflexive relation on a finite set $A$ having $n$-elements, and let there be m ordered pairs in $R$. Then

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)

Let ${R_1}$ be a relation defined by ${R_1} = \{ (a,\,b)|a \ge b,\,a,\,b \in R\} $. Then ${R_1}$ is

Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R =\{( a , b ) \in A$ $\times A : b =| a |$ or $\left.b ^2= a +1\right\}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is $........$.

Let $A = \{1, 2, 3, 4\}$ and let $R= \{(2, 2), (3, 3), (4, 4), (1, 2)\}$ be a relation on $A$. Then $R$ is