Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $R = \{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}$. Find the domain of $R$.

Let $T$ be the set of all triangles in a Euclidean plane and a relation $R$ on $T$ is defined as $aRb$ if and only if $a \sim b$ (where $a \sim b$ denotes that triangle $a$ is similar to triangle $b$) for all $a, b \in T$. Then $R$ is:

On the set $R$ of real numbers,the relation $\rho$ is defined by $x \rho y$ if $x > |y|$. Which of the following statements is true regarding the properties of $\rho$?

Check whether the relation $R$ in $\mathbb{R}$ defined by $R = \{(a, b) : a \leq b^3\}$ is reflexive,symmetric,or transitive.

The relation $S$ in the set $R$ of real numbers,defined as $S = \{(a, b) : a < b^2\}$ is a . . . . . . relation.

Let $T$ be the set of all triangles in a plane with $R$ a relation in $T$ given by $R = \{(T_1, T_2) : T_1 \text{ is congruent to } T_2\}$. Show that $R$ is an equivalence relation.