MA19.FM.5

Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.5

Prove a statement indirectly by proving the contrapositive of the statement.

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
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