Let $A = \{a, b, c\}$. The number of equivalence relations on $A$ containing $(b, c)$ is:

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$. Then the relation $R = \{(x, y) \in A \times A : x + y = 7\}$ is

If a relation $R$ on the set $\{1, 2, 3\}$ is defined by $R = \{(1, 1)\}$,then $R$ 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

Give an example of a relation which is reflexive and transitive but not symmetric.

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: