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

Let $A$ and $B$ be subsets of a set $X$. Then,

If $A = \{ x : x \text{ is an integer and } x^2 - 9 = 0 \}$,$B = \{ x : x \text{ is a natural number and } 2 \leq x < 5 \}$,and $C = \{ x : x \text{ is a prime number } \leq 4 \}$,then $(B - C) \cup A$ is:

$A$ 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?

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 $A-C$.

Which Venn diagram represents the truth of the statement "Some teenagers are not dreamers"?