$R = \{(\pi, \pi), (\pi^2, \pi^2), (\pi^3, \pi^3), (\pi, \pi^2), (\pi^2, \pi^3)\}$ is defined on the set $A = \{\pi, \pi^2, \pi^3\}$. Then $R$ is . . . . . . .

Show that the relation $R$ in the set $Z$ of integers given by $R = \{(a, b) : 2 \text{ divides } a - b\}$ is an equivalence relation.

For a set $A = \{1, 2, 3\}$,a relation $R = \{(1, 2), (2, 3)\}$ is defined. What is the minimum number of ordered pairs that must be added to $R$ to make it an equivalence relation?

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 $A = \{1, 2, 3, 4\}$ and $R$ be a relation on $A$,given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is:

Show that the relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R =\{(a, b):|a-b| \text{ is even}\}$ is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to each other and all the elements of $\{2,4\}$ are related to each other,but no element of $\{1,3,5\}$ is related to any element of $\{2,4\}$.