Domain of $f(x) = (x^2 - 1)^{-1/2}$ is

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

In a class of $100$ students, the number of students who passed in English only is $46$, in Maths only is $46$, and in Commerce only is $58$. The number of students who passed in English and Maths is $16$, in Maths and Commerce is $24$, and in English and Commerce is $26$. The number of students who passed in all three subjects is $7$. Find the number of students who failed in all the subjects.

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

The domain of the function $f(x) = \ln(x - [x])$ is

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