Let $R$ be a relation defined on the set $\{1,2,3,4\} \times \{1,2,3,4\}$ by $R = \{((a,b), (c,d)) : 2a + 3b = 3c + 4d\}$. Then the number of elements in $R$ is:

Let $A = \{1, 2, 3\}$. The number of equivalence relations on $A$ containing $(1, 2)$ is . . . . . . .

Let $R_{1} = \{(a, b) \in N \times N : |a - b| \leq 13\}$ and $R_{2} = \{(a, b) \in N \times N : |a - b| \neq 13\}$. Then on $N$:

Let $R$ be the relation in the set $N$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Choose the correct answer.

Consider the relation $R$ on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab > 0$. Then, among the statements:
$I$. The number of elements in $R$ is $17$
$II$. $R$ is an equivalence relation

In a plane,two points $P$ and $Q$ are related if $OP = OQ$,where $O$ is a fixed point. The relation is: