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CS 2050 - Chapt 1
Proofs
9
Computer Science
Undergraduate 2
02/07/2013

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Cards

Term
Even Definition
Definition

n is even if n = 2k     k ∈ ℤ

 

Term
Odd Definition
Definition
n is odd if n = 2k + 1     k ∈ ℤ
Term
Rational Definition
Definition
r is rational if r = a   a,b ∈ ℤ, b ≠ 0
Term
Direct Proof
Definition
  1. Assume p
  2. logic + math
  3. conclude q
Term
Contraposition Proof
Definition

p → q

¬ q → ¬ p

  1. Assume ¬ q
  2. logic + math
  3. conclude ¬ p therefore p → q
Term
Contradiction Proof
Definition
  1. Assume the statement is False
  2. Show p → q ≡ ¬ p ∨ q
Term
Counterexample Proof
Definition
  1. Assume ∀x P(x) is false. 
  2. Math + logic
  3. Conclude ∃x ¬P(x).
To disprove.
Term
Exhaustive Proof
Definition
Check EACH value individually.
Term
Cases Proof
Definition
  1. Break down into distinct groups (exp. true and false; even and odd )
  2. Prove each case.
  3. Conclude it is proved in general
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