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:

In the set of natural numbers,the relation "is less than" is:

Let $A = \{-2, -1, 0, 1, 2, 3\}$. Let $R$ be a relation on $A$ defined by $x R y$ if and only if $y = \max \{x, 1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added to $R$ to make it reflexive and symmetric,respectively. Then $l + m + n$ is equal to

For $\alpha \in N$,consider a relation $R$ on $N$ given by $R = \{(x, y) : 3x + \alpha y \text{ is a multiple of } 7\}$. The relation $R$ is an equivalence relation if and only if:

Let $A$ be the set of all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ and $R$ be a relation on $A$ such that $R =\{( f , g ): f(0)= g (1) \text{ and } f(1)= g (0)\}$. Then $R$ is:

Let $A = \{2, 4, 6, 8\}$. $A$ relation $R$ on $A$ is defined by $R = \{(2, 4), (4, 2), (4, 6), (6, 4)\}$. Then $R$ is: