https://file.aiquickdraw.com/mathbot/file/1729081432491om6my797.jpg

https://file.aiquickdraw.com/mathbot/file/1729081432492ydotivlv.jpg

Let's go through the statements one by one and determine which pairs are logically true or false.

### The Original Conditional Statement:
**A. Conditional**: If an animal is a lion, then it is a cat that can roar.

This is the given statement and serves as the baseline.

### Other Statements Derived from the Conditional:
1. **B. Converse**: If an animal is a cat that can roar, then it is a lion.
   - The converse swaps the hypothesis and the conclusion. However, this is **false**, because other animals (like tigers) are also cats that can roar but are not lions.

2. **C. Inverse**: If an animal is not a lion, then it is not a cat that can roar.
   - The inverse negates both parts of the conditional. This statement is **false** because other cats (such as tigers) can roar but are not lions.

3. **D. Contrapositive**: If an animal is not a cat that can roar, then it is not a lion.
   - The contrapositive negates both the hypothesis and the conclusion and reverses them. This is **true**, because if an animal cannot roar and is not a cat, it logically cannot be a lion.

### Conclusion for Question 9: 
The logically **true** pairs are:
- A and D.

### Conclusion for Question 10:
The logically **false** pairs are:
- B and C.

Would you like a more detailed explanation of any part of this? Here are some related questions you could explore:

1. How do you derive the inverse from a conditional statement?
2. What is the relationship between the converse and contrapositive?
3. Can there be situations where the converse is true?
4. Why is the contrapositive always logically equivalent to the original conditional?
5. How does the truth of the inverse relate to the original conditional?

**Tip:** Remember, the contrapositive of a true conditional statement is always true, but the converse and inverse are not necessarily true.

Which pairs of statements are logically true or false based on conditional, converse, inverse, and contrapositive logic?

Learn how to evaluate conditional statements and their converse, inverse, and contrapositive. This problem walks through logical reasoning to determine which pairs of statements are logically true or false, using concepts of logical equivalence. Suitable for Grades 9-12.

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