Contrapositive
Definition
The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion, then reversing them. If the original statement is 'If P, then Q,' the contrapositive is 'If not Q, then not P.'
5 Must Know Facts For Your Next Test
- The contrapositive of a statement is always logically equivalent to the original statement.
- To form the contrapositive, you must negate both parts of the original conditional statement and switch their order.
- If a conditional statement is true, its contrapositive must also be true.
- The process of forming a contrapositive can help in proving theorems and solving logical problems.
- Contrapositives are used extensively in mathematical proofs and logic reasoning.
Review Questions
- How do you form the contrapositive of 'If it rains, then we will cancel the picnic'?
- Why is the contrapositive considered logically equivalent to its original statement?
- What happens to the truth value of a conditional statement if its contrapositive is false?
"Contrapositive" appears in:
Related terms
Conditional Statement: A logical statement that has two parts, an antecedent (if part) and a consequent (then part).
Inverse: Formed by negating both the hypothesis and conclusion of a conditional statement without switching their order.
Converse: Formed by reversing the hypothesis and conclusion of a conditional statement.
