Question

This is for discrete math: The records of 100 Texas A&M students show the following courses...

This is for discrete math:

The records of 100 Texas A&M students show the following courses were taken:

- 41 students took Marketing

- 48 students took Writing

- 53 students took History

- 18 students took History and Marketing

- 21 students took Marketing and Writing

- 7 students took all 3 courses

- 9 students took none of these course

How many students took only History?

How many students took Marketing and Writing, but not History?

Please show work, and please include a Venn diagram because that helps me understand it. I currently don't see how it's possible to know the answers to these questions because it is unknown how many students took Writing and History.

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Answer #1

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100 Texas A&M students n(U)=100

41 students took Marketing n(M) = 41

48 students took Writing n(W) = 48

53 students took History n(H) = 53

18 students took History and Marketing |H ∩M| = 18

21 students took Marketing and Writing |M ∩W| = 21

7 students took all 3 courses |H ∩M ∩W| = 7

9 students took none of these courses |N| = 9

1)

Step 1: U - |N| = 100-9 = 91

Step 2: |H| + |M| + |W| - |H ∩M| - |M ∩W| - |H ∩W| + |H ∩M ∩W| = 91

53+41+48-18-21-|H ∩W|+7=91

|H ∩W| = 19

Step 4: |H| - |H ∩W| - |H ∩M| + |H ∩M ∩W| =53-19-18+7 = 23

23 students taking history only

2)

|M ∩W| -|H ∩M ∩W| = 21-7 = 14

14 students taking Marketing and Writing only

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