Find the union of each of the following pairs of sets:
$A = \{a, e, i, o, u\}$,$B = \{a, b, c\}$

If $A = \{3, 5, 7, 9, 11\}$,$B = \{7, 9, 11, 13\}$,$C = \{11, 13, 15\}$,and $D = \{15, 17\}$,find $(A \cap B) \cap (B \cup C)$.

$A$ class has $175$ students. The following data shows the number of students opting for one or more subjects: Mathematics $100$,Physics $70$,Chemistry $40$; Mathematics and Physics $30$,Mathematics and Chemistry $28$,Physics and Chemistry $23$; Mathematics,Physics,and Chemistry $18$. How many students have opted for Mathematics alone?

In a class of $140$ students numbered $1$ to $140$,all even-numbered students opted for the Mathematics course,those whose number is divisible by $3$ opted for the Physics course,and those whose number is divisible by $5$ opted for the Chemistry course. The number of students who did not opt for any of the three courses is:

If $A=\{3, 6, 9, 12, 15, 18, 21\}, B=\{4, 8, 12, 16, 20\}, C=\{2, 4, 6, 8, 10, 12, 14, 16\}, D=\{5, 10, 15, 20\};$ find $A-D$.

Let $E, F$ and $G$ be three events having probabilities $P(E) = \frac{1}{8}, P(F) = \frac{1}{6}$ and $P(G) = \frac{1}{4}$,and let $P(E \cap F \cap G) = \frac{1}{10}$. For any event $H$,if $H^C$ denotes its complement,then which of the following statements is(are) $TRUE$?
$(A) P(E \cap F \cap G^C) \leq \frac{1}{40}$
$(B) P(E^C \cap F \cap G) \leq \frac{1}{15}$
$(C) P(E \cup F \cup G) \leq \frac{13}{24}$
$(D) P(E^C \cap F^C \cap G^C) \leq \frac{5}{12}$