PL 120

Symbolic Logic I

    Replacement Rules


Transform each of the following formulae into a logically equivalent formula using the replacement rule indicated.


 1.  C (A B)                   Contraposition (main conditional only)


 2.  C (A B)                   Material Implication (subordinate conditional)


 3.  C (A B)                   Material Implication  (all conditionals)


 4.  C (A B)                   Exportation


 5.  ~ (C D)                           DeMorgan's Law


 6.  ~[(E F) G]                    DeMorgan's Law


 7.  H (I v J)                        Distribution


 8.  (K L) (L K)          Material Equivalence


 9.  (K L) (L K)          Material Implication (twice)


10.  (K L) (M N)         Contraposition (twice)


11.  ( A B) (C v D)          Material Implication


12.  (A B) (C v D)           Contraposition


13.  (A B) (C v D)           Exportation


14.  ~((A B) v (C v D))        DeMorgan (once)


15.  ~P ~(S T)                  Contraposition 

16.  Use exportation on the result of 15.