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)