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

Let $R$ be the relation on the set $\mathbb{R}$ of all real numbers defined by $a \ R \ b$ if $|a - b| \le 1$. Then $R$ is

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

Let $A = \{p, q, r\}$. Which of the following is an equivalence relation on $A$?

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

Let $X = R \times R$. Define a relation $R$ on $X$ as: $(a_1, b_1) R (a_2, b_2) \Leftrightarrow b_1 = b_2$. Statement-$I$: $R$ is an equivalence relation. Statement-$II$: For some $(a, b) \in X$,the set $S = \{(x, y) \in X : (x, y) R (a, b)\}$ represents a line parallel to $y = x$. In the light of the above statements,choose the correct answer from the options given below: