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Answer :
Final answer:
A total of 62 students read at least one of the magazines surveyed, while 38 students did not read any of the three publications. We used the inclusion-exclusion principle in set theory to arrive at these numbers.
Explanation:
Analyzing the Survey Results
To solve the problem, we need to find the total number of students who read at least one magazine and how many read none of the three publications. We will use the principle of inclusion-exclusion in set theory.
Step 1: Define the Sets
- A = Students who read Time Magazine
- B = Students who read Newspaper
- C = Students who read US News
Step 2: Use Inclusion-Exclusion Formula
The formula for the union of three sets is given by:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
Substituting in the values we have:
|A| = 40, |B| = 30, |C| = 25
|A ∩ B| = 15, |A ∩ C| = 12, |B ∩ C| = 10
|A ∩ B ∩ C| = 4
Plugging in these numbers:
|A ∪ B ∪ C| = 40 + 30 + 25 - 15 - 12 - 10 + 4
Calculating this results in:
|A ∪ B ∪ C| = 40 + 30 + 25 - 15 - 12 - 10 + 4 = 62
Step 3: At least one magazine
Therefore, 62 students read at least one magazine.
Step 4: Finding Students Who Read None
Next, to find how many students read none of these publications, we simply subtract the number of students who read at least one publication from the total surveyed students:
Total students = 100
Students reading none = 100 - 62 = 38
Thus, 38 students read none of these three publications.
Learn more about student survey results here:
https://brainly.com/question/40383440
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