SET THEORY

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  1. 3. In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?
  2. 4. A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets?
  3. 5. In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects?
  4. 8. The part of venn diagram where common things exist.
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  1. 1. In a class of 50 students, 18 takes Chorus, and 26 take Band, and 2 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band?
  2. 2. Of 60 students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, 16 do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. What are the maximum number of people who could have done Chemistry only?
  3. 6. In a school of 30 students, 8 students are in the band, 20 students are on sports teams, and 6 students participate in both activities. How many students are not involved in any activity?
  4. 7. 95% of the students in a class have taken Marketing, 80% have chosen Finance, 84% have chosen operations (ops), and 90% have chosen Human Resources (HR). What is the maximum percentage of people who have chosen all of the four?
  5. 9. A guidance counselor is planning schedules for 30 students. Sixteen students say they want to take French, 16 want to take Spanish, and 11 want to take Latin. Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish. How many students want French only?
  6. 10. this is an another name for an empty set.