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Propositional Logic Rules

  1. COMMUTATIVE
  2. ASSOCIATIVE
  3. DISTRIBUTIVE
  4. IDEMPOTENT (or Tautology)
  5. ABSORBTION
  6. COMPLEMENTATION
  7. LAW OF INVOLUTION
  8. LAWS OF DEMORGAN
  9. IDENTITY ELEMENTS
  10. EXCLUSIVE OR
  11. RELATION OF IMPLICATION
  12. MODUS PONENS (Rule of Detachment)
    $P \Rightarrow Q$
    $P$
    $----$
    $Q$
  13. MODUS TOLENS
    $P \Rightarrow Q$
    $\neg Q$
    $----$
    $ \neg P$
  14. RESOLUTION (Law of Syllogism)
    $P \vee Q$
    $ \neg P \vee R$
    $----$
    $Q \vee R$
  15. AND ELIMINATION
    $P \wedge Q$
    $----$
    $P$
    $Q$
  16. DISJUNCTIVE SYLLOGISM
    $P$
    $----$
    $P \vee Q$
  17. Basic Truth table:
    P  Q   V        P  Q  &
    -----------------------
    0  0   0        0  0  0
    0  1   1        0  1  0
    1  0   1        1  0  0
    1  1   1        1  1  1
    
  18. Parallel and Series Circuits
         Parallel
    
              /
          ---   ---
         |    p    |
     A --           -- B               Also know: AND Gate
         |    /     |                             OR Gate
          ---   ---
              q
    
         Series
         
           /     /
     A ---   ---   --- B
           p     q
    


Randy Latimer 2001-01-11