Let $A = \{-2, -1, 0, 1, 2, 3, 4\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $2x + y \le 2$. 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:

Let $R$ be a relation defined on $N \times N$ by $(a, b) R(c, d) \Leftrightarrow a(b + d) = c(b + d)$ is incorrect,the correct relation is $(a, b) R(c, d) \Leftrightarrow ad = bc$. Given the relation $(a, b) R(c, d) \Leftrightarrow a(b + d) = c(a + d)$ is not standard,let us analyze the relation $(a, b) R(c, d) \Leftrightarrow ad = bc$. Then $R$ is:

The minimum number of elements that must be added to the relation $R = \{(a, b), (b, c)\}$ on the set $\{a, b, c\}$ so that it becomes symmetric and transitive is:

On the power set $P(A)$ of a set $A$,the relation "is a subset of" $(\subseteq)$ is:

Show that the relation $R$ in the set $\{1, 2, 3\}$ given by $R = \{(1, 2), (2, 1)\}$ is symmetric but neither reflexive nor transitive.

Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $R = \{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}$. Find the domain of $R$.