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 $A = \{0, 1, 2, \ldots, 9\}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $|x - y|$ is a multiple of $3$. Given below are two statements:
Statement $I$: $n(R) = 36$
Statement $II$: $R$ is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below:

Let $X$ be a non-void set. If $\rho_1$ and $\rho_2$ are transitive relations on $X$, then which of the following is true?

If $R = \{(6, 6), (9, 9), (6, 12), (12, 12), (12, 6)\}$ is a relation on set $A = \{3, 6, 9, 12\}$,then relation $R$ is

Let $R$ be a relation over the set $N \times N$ and it is defined by $(a, b)R(c, d) \iff a + d = b + c$. Then $R$ is

The number of relations, defined on the set ${a, b, c, d}$, which are both reflexive and symmetric, is equal to: