In a class of $50$ students,$35$ opted for Mathematics and $37$ opted for Biology. How many have opted for both Mathematics and Biology? How many have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects).

The range of $f(x) = \sec \left( \frac{\pi}{4} \cos^2 x \right)$ for $-\infty < x < \infty$ is

If $U = \{a, b, c, d, e, f\}$,$A = \{a, b, c\}$,$B = \{c, d, e, f\}$,and $C = \{c, d, e\}$,find $(A \cup B) \cup C$.

$A$ class has $175$ students. The following data shows the number of students obtaining 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 offered Mathematics alone?

If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$,then $(A \cap B) \cup (A \cap C)$ is equal to

Write down the power set of the set ${0}.$