The relation "less than" in the set of natural numbers is

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $N$ of natural numbers defined as
$R = \{(x, y) : y = x + 5 \text{ and } x < 4\}$

Let $A = \{1, 2, 3\}$. Then the number of equivalence relations containing $(1, 2)$ is:

Let $R$ be the relation in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3)\}$. Choose the correct answer.

$R = \{(\pi, \pi), (\pi^2, \pi^2), (\pi^3, \pi^3), (\pi, \pi^2), (\pi^2, \pi^3)\}$ is defined on the set $A = \{\pi, \pi^2, \pi^3\}$. Then $R$ is . . . . . . .

Let $r$ be a relation from $R$ (set of real numbers) to $R$ defined by $r = \{(x, y) \mid x, y \in R \text{ and } xy \text{ is an irrational number}\}$. Then,the relation $r$ is: