Let $R$ and $S$ be equivalence relations on a set $A$. Then,

Let $R$ be a relation on the set of real numbers defined by $nm \ge 0$. Then $R$ is:

The relation $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is

Let $R = \{(x,y) : x,y \in N \text{ and } x^2 - 4xy + 3y^2 = 0\}$,where $N$ is the set of all natural numbers. Then the relation $R$ is

Let $R$ be the relation in the set $N$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Choose the correct answer.

Let $A$ be the set of all students of a boys' school. Show that the relation $R$ in $A$ given by $R = \{(a, b) : a \text{ is sister of } b\}$ is the empty relation and $R^{\prime} = \{(a, b) : \text{the difference between heights of } a \text{ and } b \text{ is less than } 3 \text{ meters}\}$ is the universal relation.