Consider the sets $\phi, A=\{1,3\}, B=\{1,5,9\}, C=\{1,3,5,7,9\}$. Insert the symbol $\subset$ or $\not\subset$ between the pair of sets: $A, \ldots B$.

If $D_{30}$ is the set of all divisors of $30$,$x, y \in D_{30}$,we define $x+y=\operatorname{LCM}(x, y)$,$x \cdot y=\operatorname{GCD}(x, y)$,$x^{\prime}=\frac{30}{x}$ and $f(x, y, z)=(x+y) \cdot (y^{\prime}+z)$,then $f(2, 5, 15)$ is equal to

Show that if $A \subset B$,then $(C - B) \subset (C - A)$.

Examine whether the following statement is true or false:
$\{a, e\} \subset \{x : x \text{ is a vowel in the English alphabet}\}$

Write the set $\{ \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7} \}$ in the set-builder form.

If ${N_a} = \{an : n \in N\}$,then ${N_5} \cap {N_7} = $