Question

in a class of 50 student,18 offered mathematics, 21 offered chemistry while 16 offered biology, 7 student offered mathematics and biology, 9 student offered chemistry and biology while 5 student offered the three subject combination.
a) find the numbers of student that offered mathematics but offered neither chemistry and biology
b) the number of student who did not offer any of the three subject combination

Answer 1

Draw a Venn diagram if you like, and then recall that
(m+c+b) - (m&c+m&b+b&c) + (m&c&b) = 50 - (none)
now plug in the numbers.
(18+21+16)-(m&c+7+9)+(5) = 50 - (none)
55 - (m&c+16) + 5 = 50-(none)
39+m&c = 50-(none)
m&c = 11-(none)
Since m&c >= 0,
none <= 11
So, as long as no more than 11 people offered nothing, any value will work.

So, if there was a number you forgot to include, plug it in and find the unique solution.