Given the relation $R = \{(1, 2), (2, 3)\}$ on the set $A = \{1, 2, 3\}$,the minimum number of ordered pairs which when added to $R$ make it an equivalence relation is

For any two real numbers $\theta$ and $\phi$, we define $\theta R \phi$ if and only if $\sec^{2} \theta - \tan^{2} \phi = 1$. The relation $R$ is

Let $R$ be the real line. Let the relations $S$ and $T$ on $R$ be defined by $S = \{(x, y) : y = x + 1, 0 < x < 2\}$ and $T = \{(x, y) : (x - y) \text{ is an integer}\}$. Then:

If $R$ is a relation on the set $N$ (set of natural numbers),defined by $R = \{(x, y) : 3x + 3y = 10\}$.
Statement-$1$: $R$ is symmetric.
Statement-$2$: $R$ is reflexive.
Statement-$3$: $R$ is transitive.
Determine the correct sequence of truth values for the given statements (where $T$ means true and $F$ means false).

Let $R$ be a transitive relation on a set $A$ and $I$ be the identity relation on $A$. Then:

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