In a town with a population of $5000$,$3200$ people are egg-eaters,$2500$ are meat-eaters,and $1500$ eat both egg and meat. How many are pure vegetarians?

Which of the following is a true statement?

In a class of $140$ students numbered $1$ to $140$,all even-numbered students opted for the Mathematics course,those whose number is divisible by $3$ opted for the Physics course,and those whose number is divisible by $5$ opted for the Chemistry course. The number of students who did not opt for any of the three courses is:

If $f(x) = \frac{x - |x|}{|x|}$,then $f(-1) = $

The range of $f(x) = \cos x - \sin x$ is

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements are true?