Let $R$ be a relation on a set $A$ such that $R = R^{-1}$. Then $R$ is:

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:

If $R$ is the smallest equivalence relation on the set $\{1, 2, 3, 4\}$ such that $\{(1, 2), (1, 3)\} \subset R$,then the number of elements in $R$ is

Let $R$ be the relation in the set $\{1, 2, 3, 4\}$ given by $R = \{(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)\}$. Choose the correct answer.

Let $A$ be the non-void set of the children in a family. The relation '$x$ is a brother of $y$' on $A$ is

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