Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is

Let $H$ be the set of all houses in a village where each house is faced in one of the directions, East, West, North, South. Let $R = \{ (x,y)|(x,y) \in H \times H$ and $x, y$ are faced in same direction $\}$ . Then the relation $' R '$ 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 $S$ be set of all real numbers ; then on set $S$ relation $R$ defined as $R = \{\ (a, b) : 1 + ab > 0\ \}$ is

If $R$ is an equivalence relation on a set $A$, then ${R^{ – 1}}$ is