In a survey,it was found that $63\%$ of Americans like cheese and $76\%$ like apples. If $x\%$ of Americans like both cheese and apples,then:

$A$ and $B$ are two subsets of set $S = \{1, 2, 3, 4\}$ such that $A \cup B = S$. Then,the number of ordered pairs $(A, B)$ is:

$205$ students take an examination,of whom $105$ pass in English,$70$ students pass in Mathematics,and $30$ students pass in both. How many students fail in both subjects?

If $A = \{x \in \mathbb{R} : |x - 2| > 1\}$,$B = \{x \in \mathbb{R} : \sqrt{x^2 - 3} > 1\}$,$C = \{x \in \mathbb{R} : |x - 4| \geq 2\}$,and $\mathbb{Z}$ is the set of all integers,then the number of subsets of the set $(A \cap B \cap C)^c \cap \mathbb{Z}$ is .... .

There are $200$ individuals with a skin disorder. $120$ had been exposed to the chemical $C_{1}$,$50$ to chemical $C_{2}$,and $30$ to both the chemicals $C_{1}$ and $C_{2}$. Find the number of individuals exposed to chemical $C_{1}$ or chemical $C_{2}$.

Let $A = \{x : |x^{2} - 10| \le 6\}$ and $B = \{x : |x - 2| > 1\}$. Then: