An integer $m$ is said to be related to another integer $n$ if $m$ is a multiple of $n$. Then the relation 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:

The relation $R$ is defined on the set $N$ by $R = \{(x, y) | x, y \in N, 2x + y = 41\}$. Then $R$ is:

Let $A = \{-4, -3, -2, 0, 1, 3, 4\}$ and $R = \{(a, b) \in A \times A : b = |a| \text{ or } b^2 = a + 1\}$ be a relation on $A$. Then the minimum number of elements that must be added to the relation $R$ so that it becomes reflexive and symmetric is $........$.

Let $R$ and $S$ be two relations on a set $A$. Then which of the following is true?

Let $A = \{1, 2, 3, \ldots, 100\}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $2x = 3y$. Let $R_1$ be a symmetric relation on $A$ such that $R \subset R_1$ and the number of elements in $R_1$ is $n$. Then,the minimum value of $n$ is: