Explanation:
the 3 described groups have no overlap.
15 like Math but not English.
18 like English but not Math.
5 don't like either.
so, because there is no overlap, that is in total 38 students.
the class has 55 students.
when just looking at these subjects (liking Math or English, both or none of them), we have only one category of these 4 left : liking both of them.
that means this category must contain the remaining students : 55 - 38 = 17
1)
the just calculated 17 students like both.
2)
everybody, who only likes Math or likes both likes Math :
17 + 15 = 32
3)
in the same way : both plus English only :
17 + 18 = 35
4)
I cannot draw here, but this would consist of 2 circles that overlap in the middle.
one circle is for Math, the other for English.
now, you have 2 choices for the meaning of the circles:
1. people in the circle like the subject
2. people in the circle do not like the subject
it is important that both circles have the same type of meaning (like or dislike).
if you pick the first option (like), then in the non-overlapped part of Math would be 15, in the non-overlapped part of English 18. and in the center, the overlapping, there would be 17.
the remaining 5 students (not liking either) would not be in the diagram.
if you pick the second option (dislike), then in the non-overlapped part of Math would be 18, in the non-overlapped part of English 15, and in the overlapping center 5.
the remaining 17 students (liking both) would not be in the diagram.