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In a group of 50 students, 30 like Math, 25 like Science, and 10 like both. How many students do not like either?
5
10
15
20
5
Apply the Principle of Inclusion-Exclusion: Total = Math + Science - Both + Neither. Subtract the union from the total students to find those who like neither.
Apply the Principle of Inclusion-Exclusion: Total = Math + Science - Both + Neither. Subtract the union from the total students to find those who like neither.
Calculate students liking at least one subject
Using the formula: Students liking Math or Science = (Students liking Math) + (Students liking Science) - (Students liking both). This is 30 + 25 - 10 = 45.
Calculate students liking neither subject
Subtract the result (45) from the total group size (50). So, 50 - 45 = 5.
B: 10 is wrong because it fails to subtract the overlap of 10 from the total of 30+25. C: 15 is wrong because it implies an incorrect union calculation of 35 instead of 45. D: 20 is wrong because it incorrectly treats the 10 overlapping students as liking neither.
A is correct because the total number of students who like at least one subject is 45, meaning 5 out of 50 students like neither subject.
Whenever you see 'both' in a grouping problem, always subtract that intersection once so you don't double-count the students who overlap between categories.
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