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.
Homework Answers
Answer #1
Pls, give thumbs up.
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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