If $A = \{1, 2, 3, \dots, m\}$,then the total number of reflexive relations that can be defined from $A \to A$ is:

Show that the relation $R$ defined in the set $A$ of all polygons as $R = \{(P_{1}, P_{2}) : P_{1} \text{ and } P_{2} \text{ have the same number of sides}\}$,is an equivalence relation. What is the set of all elements in $A$ related to the right-angled triangle $T$ with sides $3, 4, \text{ and } 5$?

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

Let $I$ be the set of positive integers. $R$ is a relation on the set $I$ given by $R = \{(a, b) \in I \times I \mid \log_2(a/b) \text{ is a non-negative integer} \}$. Then $R$ is:

For the real numbers $x$ and $y$, we define the relation $p$ as $x p y$ if $x-y+\sqrt{2}$ is an irrational number. Then the relation $p$ is

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