Let $R = \{ (3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6) \}$ be a relation on the set $A = \{ 3, 6, 9, 12 \}$. The relation is

Let $A = \{2, 3, 5, 7, 9\}$. Let $R$ be the relation on $A$ defined by $xRy$ if and only if $2x \le 3y$. Let $l$ be the number of elements in $R$, and $m$ be the minimum number of elements required to be added in $R$ to make it a symmetric relation. Then $l + m$ is equal to:

Let $R$ be the real line. Let the relations $S$ and $T$ on $R$ be defined by $S = \{(x, y) : y = x + 1, 0 < x < 2\}$ and $T = \{(x, y) : (x - y) \text{ is an integer}\}$. Then:

Let a relation $R$ on $N \times N$ be defined as: $(x_1, y_1) R (x_2, y_2)$ if and only if $x_1 \leq x_2$ or $y_1 \leq y_2$. Consider the two statements:
$(I)$ $R$ is reflexive but not symmetric.
$(II)$ $R$ is transitive.
Then which one of the following is true?

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 $R = \{ (x,y) | (x,y) \in H \times H \text{ and } x, y \text{ are faced in same direction} \}$. Then the relation $R$ is

In $\mathbb{R}$, a relation $p$ is defined as follows: $\forall a, b \in \mathbb{R}$, $a \ p \ b$ holds if $a^2-4ab+3b^2=0$. Then: