$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then ${R^{ - 1}}$ is

Let $R$ be a relation on $N$ defined by $x + 2y = 8$. The domain of $R$ is

If $\mathrm{R}$ 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 $\mathrm{R}$ is

Let $R$ be a relation on the set $N$ be defined by $\{(x, y)| x, y \in N, 2x + y = 41\}$. Then $R$ is

Let $R$ be the relation on the set $R$ of all real numbers defined by $a \ R \ b$ if $|a - b| \le 1$. Then $R$ is

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is