Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $A$ such that $\mathrm{R} \subset \mathrm{S}$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is...............

Consider the following two binary relations on the set $A= \{a, b, c\}$ : $R_1 = \{(c, a) (b, b) , (a, c), (c,c), (b, c), (a, a)\}$ and $R_2 = \{(a, b), (b, a), (c, c), (c,a), (a, a), (b, b), (a, c)\}.$ Then

Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is

Give an example of a relation. Which is Reflexive and transitive but not symmetric.

For $\alpha \in N$, consider a relation $R$ on $N$ given by $R =\{( x , y ): 3 x +\alpha y$ is a multiple of 7$\}$.The relation $R$ is an equivalence relation if and only if.

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)