Let $A=\{1,2,3, \ldots 20\}$. Let $R_1$ and $R_2$ two relation on $\mathrm{A}$ such that $\mathrm{R}_1=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}$ is divisible by $\mathrm{a}\}$ $\mathrm{R}_2=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}$ is an integral multiple of $\mathrm{b}\}$. Then, number of elements in $R_1-R_2$ is equal to_____.

Give an example of a relation. Which is Reflexive and transitive but not symmetric.

$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then ${R^{ - 1}}$ is

Let $f: X \rightarrow Y$ be a function. Define a relation $R$ in $X$ given by $R =\{(a, b): f(a)=f(b)\} .$ Examine if $R$ is an equivalence relation.

Given the relation $R = \{(1, 2), (2, 3)\}$ on the set $A = {1, 2, 3}$, the minimum number of ordered pairs which when added to $R$ make it an equivalence relation is

$A$ relation $R$ is defined from $\{2, 3, 4, 5\}$ to $\{3, 6, 7, 10\}$ by $xRy \Leftrightarrow x$ is relatively prime to $y$. Then domain of $R$ is