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In a class of 40 students, 20 play cricket, 15 play football, and 5 play both. How many students play neither?
5
10
15
20
10
To find the number of students who play neither sport, we apply the fundamental principle of set theory for unions and intersections. The total number of students participating in at least one sport is calculated by adding the cricket players and football players, then subtracting those who play both to avoid double counting. Subtracting this active sports total from the overall class strength yields ten students.
To find the number of students who play neither sport, we apply the fundamental principle of set theory for unions and intersections. The total number of students participating in at least one sport is calculated by adding the cricket players and football players, then subtracting those who play both to avoid double counting. Subtracting this active sports total from the overall class strength yields ten students.
Set theory and Venn diagram applications are standard quantitative aptitude foundations tested across RRB, SSC, and banking examinations.
Total class strength is forty students.
Twenty students play cricket and fifteen play football.
Five students play both sports and represent the intersection of both sets.
The number of students playing at least one sport is calculated as twenty plus fifteen minus five, equaling thirty.
Subtracting the thirty active students from the total class of forty gives ten students playing neither.
Option B is correct because it accurately reflects the remainder after removing union participants from the universal set.
B is correct тАФ subtracting the thirty students participating in sports from the total class size of forty results in ten students playing neither sport.
Mastering set theory fundamentals streamlines advanced data interpretation tables and logical reasoning puzzles in competitive railway exams.