Question

A survey of 100 college students who frequent the reading lounge of a university revealed the following results: 41 read Time. 34 read Newsweek. 28 read U.S. News & World Report. 16 read Time and Newsweek. 13 read Time and U.S. News & World Report. 12 read Newsweek and U.S. News & World Report. 5 read all three magazines. How many of the students surveyed read none of these magazines?

Answer 1

Answer: 33students

Step-by-step explanation:

Using set notation;

Let n(U) be total students = 100

n(T) be those that read Time = 41

n(N) be those that read Newsweek=34

n(R) be those that read U.S. News & World Report =28.

n(TnN) for readers of Time and Newsweek = 16.

n(TnR) for readers of Time and Newsweek = 13

n(NnR) for readers of Newsweek and U.S. News & World Report. =12

n(TnNnR) for readers of all three magazines. =5

n(TuNnuR)' for those that read none of the magazines=x

Using the equation in set,

n(TuNuR)' = n(T)+n(N)+n(R)-n(TnN)-n(TnR)-n(NnR)+n(TnNnR)

41+34+28-16-13-12+5= 33

Therefore 33students read none of the magazines.

Note that 'u' means union and 'n' means intersection.

Thank you!