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Status: Tags: #archivedCards/macm101 Links: Proving Theorems

Proof by Contraposition

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• For when Direct Proofs do not work
  • ex) 3n+2 is even 11-7
• Instead of proving an implication, prove the contrapositive

Steps

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• Prove P(a) → Q(a) is a tautology for a generic value a
  1. Find contrapositive
  2. Using axioms, theorems, prove that ~P(a) is true
  3. Conclude contrapositive is true
  4. Conclude implication is true
  5. Rule of Universal Generalization to infer Ax P(a) → Q(a)

**Prove that if kl is odd, then k and l are odd If k,l are both not odd, then kl is even Assume k is even K = 2a for some integer a KL = (2a)L, associative law of multiplication for integers KL = 2(aL), aL is integer, aL = m KL = 2m KL is even

Backlinks

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list from Proof by Contraposition AND !outgoing(Proof by Contraposition)

References:

Created:: 2021-10-07 09:38