Jamie claims, "If a triangle is in Set A, then it is not isosceles." Later, Jamie discovers that `/_\MNP` is a counter example proving this claim false. Which of the following statements must be true about `/_\MNP`?

Options

A. It is isosceles and in Set A
B. It is scalene and in Set A.
C. It is obtuse and not in Set A.
D. It is scalene and not in Set A.

Answer

To solve the problem, we need to analyze Jamie's claim and the implications of the counterexample provided by triangle MNP.

### Step-by-Step Solution:

1. **Understanding Jamie's Claim**: Jamie claims, "If a triangle is in Set A, then it is not isosceles." This means that all triangles in Set A are not isosceles triangles.

**Hint**: Identify the nature of the claim and what it implies about triangles in Set A.

2. **Identifying the Counterexample**: A counterexample is an example that disproves a claim. Jamie discovers that triangle MNP is a counterexample to the claim. This means that triangle MNP must be isosceles and also part of Set A.

**Hint**: Recall that a counterexample must directly contradict the original claim.

3. **Analyzing Triangle MNP**: Since triangle MNP is a counterexample, it must satisfy two conditions:
- It is isosceles (meaning it has at least two equal sides).
- It is in Set A (meaning it belongs to the set that Jamie initially claimed does not contain isosceles triangles).

**Hint**: Think about the definitions of isosceles triangles and what it means for a triangle to belong to a specific set.

4. **Evaluating the Statements**: Now, we need to evaluate the statements provided in the options to determine which must be true about triangle MNP. The only statement that aligns with our findings is that triangle MNP is isosceles and in Set A.

**Hint**: Compare each statement with the conclusions drawn from the counterexample.

5. **Concluding the Solution**: The only statement that must be true about triangle MNP is that it is isosceles and in Set A. Any other statement that suggests it is scalene or not in Set A contradicts the nature of the counterexample.

**Hint**: Remember that a valid conclusion must consistently support the disproving of the original claim.

### Final Answer:
Triangle MNP is isosceles and in Set A.