What are two math examples and their contrapositive statements 

In logic, the contrapositive of an implication \( p \rightarrow q \) is \( \neg q \rightarrow \neg p \), where \( \neg p \) means "not \( p \)" and \( \neg q \) means "not \( q \)." A statement and its contrapositive are logically equivalent. Here are two examples with their contrapositive statements:

### Example 1:
- **Original statement**: "If it rains, then the ground will be wet."  
  - \( p \): "It rains."  
  - \( q \): "The ground is wet."  
- **Contrapositive**: "If the ground is not wet, then it does not rain."  
  - \( \neg q \): "The ground is not wet."  
  - \( \neg p \): "It does not rain."

### Example 2:
- **Original statement**: "If a number is even, then it is divisible by 2."  
  - \( p \): "The number is even."  
  - \( q \): "The number is divisible by 2."  
- **Contrapositive**: "If a number is not divisible by 2, then it is not even."  
  - \( \neg q \): "The number is not divisible by 2."  
  - \( \neg p \): "The number is not even."

Would you like more details or examples on this topic? Here are some related questions for further practice:

1. What is the contrapositive of "If a triangle is equilateral, then it has equal angles"?
2. How can you prove that a statement is logically equivalent to its contrapositive?
3. Can a statement be true if its contrapositive is false?
4. How do you form the contrapositive for complex compound statements?
5. What is the contrapositive of "If a student studies, they will pass the exam"?

**Tip**: The contrapositive is always logically equivalent to the original statement, meaning both are either true or false together.

What are two math examples and their contrapositive statements?

Explore two mathematical examples and their contrapositive statements in this comprehensive guide. Understand the logic behind implications and contrapositive formation. Suitable for high school students (Grades 9-12) learning about logical equivalence.

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