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In a class 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
To find the number of students who do not like either subject, we use the principle of inclusion-exclusion. The total number of students liking at least one subject is calculated by adding those who like Math and Science, then subtracting those who like both, yielding 45 students. Subtracting this value from the total strength of 50 reveals that 5 students do not like either subject.
To find the number of students who do not like either subject, we use the principle of inclusion-exclusion. The total number of students liking at least one subject is calculated by adding those who like Math and Science, then subtracting those who like both, yielding 45 students. Subtracting this value from the total strength of 50 reveals that 5 students do not like either subject.
Set theory and Venn diagram principles serve as the quantitative bedrock for logical reasoning and data interpretation sections in Indian competitive examinations such as RRB, SSC, and UPSC Civil Services CSAT.
Total class strength is 50 students.
Students liking Math or Science or both are calculated using n(M union S) = n(M) + n(S) - n(M intersection S).
Subtracting the union from total students gives the remaining count of 5.
The inclusion-exclusion principle prevents double-counting elements that belong to multiple sets.
Option B (10) represents a failure to subtract the intersection.
Option C (15) and Option D (20) arise from arithmetic errors during set calculations.
A is correct тАФ Subtracting the 45 students who like at least one subject from the total of 50 gives 5 students who like neither.
Mastering set theory fundamentals heavily aids in solving complex Data Interpretation Venn diagram sets frequently featured in RRB Technician and NTPC examinations.