Unpacked Content
Knowledge
Students know:
- A contrapositive is formed by negating both the hypothesis/antecedent and conclusion/consequent and reversing the direction of inference.
- Proofs can be constructed by assuming that a hypothesis/antecedent is true and deducing that the conclusion/consequent is true.
Skills
Students are able to:
- Write the contrapositive statement for a conditional statement such as a property of integers or other mathematical properties.
- Construct a logical argument to prove a statement (such as a property of integers) is true by proving the contrapositive.
Understanding
Students understand that:
- The contrapositive of a statement is logically equivalent to a statement.
- A statement can be shown to be true by the laws of logic by proving that its contrapositive is true.
Vocabulary
- Contrapositive
- Proof by contrapositive
- Indirect proof
- hypothesis/antecedent
- Conclusion/consequent
