Inclusion–Exclusion Simple Case – UGC NET Question

To find how many students like at least one of the two subjects, we use the inclusion–exclusion principle. We add those who like each subject and subtract those counted twice in the overlap: 22 + 18 − 10 = 30 students. These 30 students like Mathematics, Science or both.

Option A:
Option A, 30, is the direct result of applying inclusion–exclusion and correctly represents the number who like at least one of the two subjects.

Option B:
Option B, 32, would correspond to assuming an overlap of 8 instead of 10, which contradicts the given overlap and misuses the data.

Option C:
Option C, 40, assumes that every student likes at least one of the subjects, which is not stated and need not be true.

Option D:
Option D, 50, exceeds the total number of students in the group, so it is impossible.