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)

     ~(A B)→~C

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

      C (~A v B)

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

       ~C v (~A v B)

 4.  C (A B)                   Exportation

      (C  A) B

 5.  ~ (C D)                           DeMorgan's Law

       (~C v ~D)

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

       ~(E F) v ~G

 7.  H (I v J)                        Distribution

      (H v I) (H v J)

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

     (K ↔ L)

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

     (~K v L) (~L v K)

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

      (~L ~K) (~N ~M)

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

        ~( A B) v (C v D)

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

       ~(C v D) ~( A B)

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

         A (B (C v D))

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

        ~(A B) ~(C v D)

15.  ~P ~(S T)                  Contraposition

        (S T) P

16.  Use exportation on the result of 15.

           S (T P)