Let $\rho$ be a relation defined on $N$,the set of natural numbers,as $\rho = \{(x, y) \in N \times N : 2x + y = 41\}$. Then:

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 :-

For any two real numbers $a$ and $b$,we define $a R b$ if and only if $\sin ^{2} a+\cos ^{2} b=1$. The relation $R$ 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

The relation $R = \{(a, a), (b, b), (c, c), (a, b), (b, a)\}$ is defined on the set $A = \{a, b, c\}$. Then $R$ is . . . . . . .

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