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Let's go over the problem step by step and solve it.

### Given Data:
- Total number of college students surveyed = 71
- 35 got the news from news websites.
- 23 got the news from social media.
- 6 got the news from both news websites and social media.

### We need to find the following:
1. How many got the news from **only** news websites?
2. How many got the news from **only** social media?
3. How many got the news from **either** news websites or social media?
4. How many did **not** get the news from either news websites or social media?

### Venn Diagram Setup:
Let:
- \( N \) be the set of students who got the news from **news websites**.
- \( S \) be the set of students who got the news from **social media**.
- \( N \cap S \) represents those who got the news from both news websites and social media.

We know:
- \( |N| = 35 \) (total who got news from news websites),
- \( |S| = 23 \) (total who got news from social media),
- \( |N \cap S| = 6 \) (who got news from both).

### Calculations:

#### 1. Number who got news from **only news websites**:
This is \( |N| - |N \cap S| \):
\[
\text{Only News Websites} = 35 - 6 = 29
\]

#### 2. Number who got news from **only social media**:
This is \( |S| - |N \cap S| \):
\[
\text{Only Social Media} = 23 - 6 = 17
\]

#### 3. Number who got news from **either news websites or social media**:
This is the union of both sets, \( |N \cup S| \):
\[
|N \cup S| = |N| + |S| - |N \cap S| = 35 + 23 - 6 = 52
\]

#### 4. Number who did **not** get the news from either source:
This is the complement of the union:
\[
\text{Neither} = 71 - |N \cup S| = 71 - 52 = 19
\]

### Final Answers:
1. Number who got news from only news websites = **29**
2. Number who got news from only social media = **17**
3. Number who got news from either source = **52**
4. Number who did not get news from either source = **19**

---

Do you need further details or explanations?

Here are 5 related questions to think about:
1. What would happen if more students got the news from both sources? How would the answers change?
2. What if the number of students surveyed was different—how would that impact the solution?
3. Could a student belong to neither category (news websites or social media)? What implications does this have?
4. How could the information be represented visually using a Venn diagram?
5. How can the concepts of union and intersection be applied to real-world problems beyond this scenario?

**Tip**: When solving problems involving sets, always subtract the intersection to avoid counting elements twice!

A survey of 71 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 35 got the news from news websites, 23 from social media, and 6 from both news websites and social media. Construct a Venn diagram and determine the cardinality for each region.

Learn how to solve a set theory problem using Venn diagrams. A survey of 71 students provides insights on how many students get news from either news websites or social media, including cardinality calculations for both sets. Suitable for high school students studying Venn diagrams and set theory.

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