Discrete Structures

• Conjunction


  p, q, THEREFORE p AND q
• Modus Ponens


  p -> q, p, THEREFORE q
• Modus Tollens


  p -> q, NOT q, THEREFORE NOT p
• Specialization


  p AND q, THEREFORE p

  p AND q, THEREFORE q
• Generalization


  p THEREFORE p OR q

  q THEREFORE p OR q
• Elimination


  p OR q, NOT p, THEREFORE q

  p OR q, NOT q, THEREFORE p
• Transitivity


  p -> q, q -> r, THEREFORE p -> r
• Contradiction Rule


  NOT p -> c, THEREFORE p
• Division into Cases


  p OR q, p -> r, q -> r, THEREFORE r
• Converse of p -> q


  q -> p
• Inverse of p -> q


  NOT p -> NOT q
• Contrapositive of p -> q


  NOT q -> NOT p
• Negation of p -> q


  p AND NOT q
• p -> q is also

  NOT p OR q