Propositional Logic: Proof Strategies (Kartei)

8 Karteikarten

• 1
  The conclusion is a literal (e.g. p)

  - Constructive proof; usually no additional assumptions ...
• 2
  The conclusion is a negated literal (e.g. ¬p)

  - At least one RAA necessary # Assume ¬conclusion # Try ...
• 3
  The conclusion is a disjunction (p v q).

  # Assume ¬(p v q). # Try to prove one of the disjuncts p ...
• 4
  The conclusion is a conditional (p -> q).

  # Assume p. # Try to arrive at q. # Then apply ->I. # This ...
• 5
  The conclusion is a biconditional (p <-> q).

  Two-step proof necessary (1) # Assume p # Try to arrive at ...
• 6
  The conclusion is a negated conjunction ¬(p & q).

  # Assume p and q additionally. # Usually 2 RAAs.
• 7
  The conclusion is a negated disjunction ¬(p v q).

  # Assume ¬p and ¬q additionally # Usually 2 RAAs
• 8
  The conclusion is a conjunction.

  Try to proof each conjunct, use &I.