Contraposition
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Contraposition
Contraposition is a transformation of an implication that produces a logically equivalent statement by reversing and negating its components.
Statement
- p → q ≡ ¬q → ¬p
Explanation
The implication "If p, then q" is equivalent to "If not q, then not p". This is often used in mathematical proofs.
Example
- "If it rains, then the ground is wet"
≡ "If the ground is not wet, then it does not rain".
Truth Table
| p | q | p → q | ¬q → ¬p |
|---|---|---|---|
| T | T | T | T |
| T | F | F | F |
| F | T | T | T |
| F | F | T | T |