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The problem asks for a counterexample to the conditional statement: "If you live in Springfield, then you live in Illinois."

To provide a counterexample, we need to find a situation where the person lives in Springfield, but not in Illinois. Let's analyze the options:

a. **Sara Lucas lives in Springfield.**  
   - It doesn't specify which Springfield, so this option is inconclusive as there are several Springfields in different states.
   
b. **Jonah Lincoln lives in Springfield, Illinois.**  
   - This person lives in Illinois, so this option supports the conditional, not a counterexample.

c. **Billy Jones lives in Chicago, Illinois.**  
   - This option doesn’t mention Springfield, so it’s irrelevant to the question.

d. **Erin Naismith lives in Springfield, Massachusetts.**  
   - This is a counterexample because Erin lives in Springfield, but *not* in Illinois. She lives in Massachusetts.

### Answer: **d. Erin Naismith lives in Springfield, Massachusetts.**

Would you like more details or have any questions?

Here are 5 related questions to expand on the topic:
1. What is a counterexample in logic?
2. How do conditional statements work in logic?
3. Can there be multiple counterexamples to a single conditional statement?
4. How does the truth value of a conditional statement change with a counterexample?
5. What are other famous examples of conditional statements in mathematics?

**Tip:** Always ensure to understand the definitions in a conditional statement to identify possible exceptions or counterexamples effectively!

Which statement is a counterexample for the following conditional?
If you live in Springfield, then you live in Illinois.
a. Sara Lucas lives in Springfield.
b. Jonah Lincoln lives in Springfield, Illinois.
c. Billy Jones lives in Chicago, Illinois.
d. Erin Naismith lives in Springfield, Massachusetts.

Understand how to identify a counterexample for the conditional statement: 'If you live in Springfield, then you live in Illinois.' This problem explores logical reasoning and conditional statements, suitable for students in Grades 7-9. Learn how the example of Erin Naismith living in Springfield, Massachusetts, serves as a counterexample.

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