66 Freshmen were interviewed about the classes they weretaking this semester. 27

Question

66 Freshmen were interviewed about the classes they weretaking this semester. 27 said they were taking science 23 said math 19 said english 10 said they were taking both science and math 4 said science and english 4 said math and english 2 said all three classes How many students are not taking any science, math orenglish? How many students are taking exactly one of science, math, orenglish? 66 Freshmen were interviewed about the classes they weretaking this semester. 27 said they were taking science 23 said math 19 said english 10 said they were taking both science and math 4 said science and english 4 said math and english 2 said all three classes How many students are not taking any science, math orenglish? How many students are taking exactly one of science, math, orenglish?

Explanation / Answer

let set A be those who are taking science, B for math, and Cfor English. n(A)=27, n(B)=23, n(C)=19, n(AB)=10,n(AC)=4,n(BC)=4,n(ABC)=2 n(AUBUC)= n(A) + n(B) + n(C)- n(AB) -n(AC) -n(BC) +n(ABC)*("U" meanunion) n(AUBUC)= 27 +23+19 - 10 -4 - 4 +2=53, therefore, students who are nottaking any science, math or english will be,(66-53)=13. Students who take onlyscience, =27 -10 -4+2 =15 Students who take onlymath, =n(B) - n(AB) -n(BC)+n(ABC) =23 -10 - 4+2 =11 Students whotake onlyenglish, =n(C) -n(CB) - n(AC)+n(ABC) =19 - 4 -4+2 =13

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