In a certain examination, 52 candidates offered biology, 60 history, 96 offered mathhematics , 21 offered biology and history, 22 offered both biology and mathematics, 16 mathematics and history. If 7 candidates offer all the three subjects find:(a) how many candidates were there for the examination

Answer 1

number(biology OR history OR mathematics) =
number(biology) + number(history) + number(math) - number(history ANS biology) - number(history AND math) - number(biology AND math) + number(biology AND history AND mathematics)

you are given each of those values, just plug in and evaluate.

Answer 2

Using what you know about the intersections of sets, and using a Venn diagram, you can see that
(52+60+96)-(21+22+16)+(7) = 156