So it is not hard just use the exclusive or definition
The students studying "violin but not clarinet", "clarinet but not violin" are the student studying either clarinet or violin.
We are told the following:
- 17 V
- 13 C
- 5 Neither
- 28 all together.
For these problems try to solve a sub-problem. To solve a bigger problem
Let try and find num_V_and_C:
28 = 5 + num_V_or_C
= 5 + num_V + num_C - Num_V_and_C
= 5 + 17 + 13 - num_V_and_C
= 35 - num_V_and_C
So 28 = 35 - num_V_and_C
=> -7 = -num_V_and_C
=> num_V_and_C = 7
stud_only_V = num_V - num_V_and_C = 10
stud_only_C = num_C - num_V_and_C = 6
either_V_or_C = stud_only_V + stud_only_C = 16