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

For a set $A = \{1, 2, 3\}$,a relation $R = \{(1, 2), (2, 3)\}$ is defined. What is the minimum number of ordered pairs that must be added to $R$ to make it an equivalence relation?

Let $S$ be the set of all real numbers. Then the relation $R = \{(a, b) : 1 + ab > 0\}$ on $S$ 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

Show that the relation $R$ in the set $A$ of all the books in a library of a college,given by $R = \{(x, y) : x \text{ and } y \text{ have the same number of pages} \}$ is an equivalence relation.

If $R$ is an equivalence relation on a set $A$,then $R^{-1}$ is not :-