The relation $R = \{(a, a), (b, b), (c, c), (a, b), (b, a)\}$ is defined on the set $A = \{a, b, c\}$. Then $R$ is . . . . . . .

Let $S = \{1, 2, 3, \ldots, 10\}$. Suppose $M$ is the set of all subsets of $S$. Then the relation $R = \{(A, B) : A \cap B \neq \phi; A, B \in M\}$ is :

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 $A$ be the set of all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ and $R$ be a relation on $A$ such that $R =\{( f , g ): f(0)= g (1) \text{ and } f(1)= g (0)\}$. Then $R$ is:

Consider the relation $R$ on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab > 0$. Then,among the statements:
$I$. The number of elements in $R$ is $17$
$II$. $R$ is an equivalence relation

The empty relation on a set $A$ is