Let $A = \{2, 4, 6, 8\}$. $A$ relation $R$ on $A$ is defined by $R = \{(2, 4), (4, 2), (4, 6), (6, 4)\}$. Then $R$ is:

Let $R$ and $S$ be two equivalence relations on a non-void set $A$. 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 $P$ be the relation defined on the set of all real numbers such that $P = \{(a,b) : \sec^2 a - \tan^2 b = 1\}$. Then $P$ is

For the real numbers $x$ and $y$, we define the relation $p$ as $x p y$ if $x-y+\sqrt{2}$ is an irrational number. Then the relation $p$ is

Let the relation $R$ on the set $M = \{1, 2, 3, \dots, 16\}$ be given by $R = \{(x, y) : 4y = 5x - 3, x, y \in M\}$. Then the minimum number of elements required to be added in $R$, in order to make the relation symmetric, is equal to