The domain of the function $f(x) = \log_{3 + x}(x^2 - 1)$ is

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 domain of $f(x) = \frac{\log_2(x + 3)}{x^2 + 3x + 2}$ is

The natural domain of the real-valued function defined by $f(x) = \sqrt{x^2 - 1} + \sqrt{x^2 + 1}$ is

If $A$ and $B$ are any two non-empty sets and $A$ is a proper subset of $B$. If $n(A) = 4$,then the minimum possible value of $n(A \Delta B)$ is (where $\Delta$ denotes the symmetric difference of set $A$ and set $B$).

In a certain town,$25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements:
$(A) \, 5\%$ families own both a car and a phone
$(B) \, 35\%$ families own either a car or a phone
$(C) \, 40,000$ families live in the town
Then,