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In a class of 40 students, 25 students like cricket, 20 students like football, and 10 students like both. How many students like neither?
5
10
15
0
5
The number of students who like at least one sport is calculated using the inclusion-exclusion principle as 25 plus 20 minus 10, which equals 35. Subtracting this union from the total class strength of 40 yields 5 students who like neither sport.
The number of students who like at least one sport is calculated using the inclusion-exclusion principle as 25 plus 20 minus 10, which equals 35. Subtracting this union from the total class strength of 40 yields 5 students who like neither sport.
Set theory and the principle of inclusion-exclusion form the foundational quantitative reasoning framework tested regularly in Indian railway and banking competitive examinations.
Total class strength represents the universal set containing all surveyed individuals.
The intersection represents students who like both cricket and football.
The difference between total students and the union of both sports gives the number of students outside both categories.
Option A (5) is correct because 40 minus 35 equals 5.
Option B, C, and D are incorrect due to calculation errors in applying the union formula.
Venn diagrams offer a graphical approach to verify counts and prevent double-counting of overlapping subsets.
A is correct тАФ 5 students like neither cricket nor football.
Mastering set theory formulas is crucial for solving complex probability and data interpretation sets efficiently in RRB exams.