In a class of 104 students a student is allowed to offer either Economics or Book keeping or Government or both.35 students offer Economics 43 offer Book keeping 59 offer Government 11 offer both Economics and Government while 9 offer all the three subjects.
(a)Draw a Venn diagram to illustrate the information .
(b)How many students offer two subjects only?
(c)How many students offer one subject?
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(a) Venn diagram:
(b) To find the number of students who offer two subjects only, we first need to add up the number of students who offer each subject:
- Economics only: 35 - 11 - 9 = 15
- Book keeping only: 43 - 9 - 11 = 23
- Government only: 59 - 11 - 9 = 39
Then, we can add up the number of students who offer only two subjects:
- Economics and Book keeping: 9
- Economics and Government: 11 - 9 = 2
- Book keeping and Government: 11 - 9 = 2
So, the total number of students who offer two subjects only is 15 + 23 + 39 + 9 + 2 + 2 = 90.
(c) To find the number of students who offer only one subject, we can add up the number of students who offer each subject only:
- Economics only: 15
- Book keeping only: 23
- Government only: 39
So, the total number of students who offer one subject only is 15 + 23 + 39 = 77.