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.