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.

Solutions