If $X = \{ 4^n - 3n - 1 : n \in N \}$ and $Y = \{ 9(n - 1) : n \in N \}$,then $X \cup Y = \dots$

Let $A = \{a, e, i, o, u\}$ and $B = \{a, i, u\}$. Show that $A \cup B = A$.

State whether the following statement is true or false. Justify your answer.
${2, 3, 4, 5}$ and ${3, 6}$ are disjoint sets.

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:

Let $A = \{ \theta : 2\cos^2 \theta + \sin \theta \le 2 \}$ and $B = \{ \theta : \frac{\pi}{2} \le \theta \le \frac{3\pi}{2} \}$,then $A \cap B$ is

$A$ die is thrown. Describe the following events: $A$: a number less than $7$,$B$: a number greater than $7$. Find $A \cap B$.