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The problem you've uploaded asks whether the information in the survey could be true:

- **Total number of students surveyed**: 241
- **Students taking Algebra**: 131
- **Students taking Biology**: 85
- **Students taking neither Algebra nor Biology**: 25

We are to determine if this setup is logically possible, and if so, how many students are taking **only** Algebra and how many are taking **only** Biology.

### Let's break it down using set theory:
We can define the following:
- Let \( A \) represent the set of students taking Algebra.
- Let \( B \) represent the set of students taking Biology.
- Let \( n(A) = 131 \) (students taking Algebra).
- Let \( n(B) = 85 \) (students taking Biology).
- Let \( n(\text{neither}) = 25 \) (students taking neither subject).

The total number of students is 241, so:
\[
n(A \cup B) + n(\text{neither}) = 241
\]
\[
n(A \cup B) = 241 - 25 = 216
\]

Now, we are looking to fill in the number of students who take only one subject, and the number who take both subjects. Let:
- \( x \) be the number of students taking both Algebra and Biology.

Thus, the number of students taking only Algebra is \( 131 - x \), and the number of students taking only Biology is \( 85 - x \).

The total number of students in both subjects:
\[
(131 - x) + (85 - x) + x = 216
\]
Simplifying:
\[
131 + 85 - x = 216
\]
\[
216 - x = 216
\]
Thus, \( x = 0 \).

### Conclusion:
- No students are taking both Algebra and Biology. 
- All students are either taking only Algebra or only Biology.

Now, the answer for option **B** could be true if the number of students taking Algebra but not Biology is **131**, and the number of students taking Biology but not Algebra is **85**.

Would you like further explanation or have any additional questions? 

Here are five related questions:
1. How would the equation change if there were 30 students taking both subjects?
2. Can you calculate how many students are in exactly one subject if 40 students take both subjects?
3. What happens if the number of students who take neither subject changes?
4. How would Venn diagrams help visualize this problem?
5. What if 100 students took neither subject? How would this affect the totals?

**Tip:** When working with set problems, using a Venn diagram or a formula can greatly simplify complex group relationships.

In a survey of 241 students, 131 were taking algebra, 85 were taking biology, and 25 were taking neither of the two subjects. Explain whether this could be true.

Explore a set theory problem involving a survey of 241 students, where 131 are taking algebra, 85 are taking biology, and 25 are taking neither subject. Learn how to determine the number of students taking only one subject using set theory principles.

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