Domain of the function $\frac{\sqrt{1 + x} - \sqrt{1 - x}}{x}$ is

Domain of the function $f(x) = \sqrt{2 - 2x - x^2}$ is

If $U = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$,$A = \{2, 4, 7\}$,$B = \{3, 5, 7, 9, 11\}$,and $C = \{7, 8, 9, 10, 11\}$,compute: $(A \cap U) \cap (B \cup C)$.

If $A = \{a, b\}$,$B = \{2, 3, 5, 6, 7\}$ and $C = \{5, 6, 7, 8, 9\}$,find $A \times (B \cap C)$.

The domain of the function $f(x) = \log (\sqrt {x - 4} + \sqrt {6 - x} )$ is

In a school,$20$ teachers teach either mathematics or physics. If $12$ of them teach mathematics and $4$ teach both subjects,then the number of teachers teaching physics is: