Introductory Logic
Quiz #7
November 4, 2005
 
Name: ________________________
R. Hammack
Score: _________


Use only the18 rules of inference to deduce the conclusions of the following arguments

1.

1.  ~A ∨ (B • C)  
2.  B ⊃ (C ⊃ D) /    A ⊃ D
3.  (B • C) ⊃ D 2, Exp
4.    A ⊃ (B • C) 1, Impl
5.    A ⊃ D 4, 3, HS
   
   
   
   
   






2.

 

1.    ~(D ∨ C) ∨ M  
2.    (M ∨ ~D) ⊃ C /   M
3.    (~D • ~C) ∨ M 1, DM
4.    M ∨ (~D • ~C) 3, Comm
5.    (M ∨ ~D) •(M ∨ ~C) 4, Dist
6.    M ∨ ~D 5, Simp
7.    M ∨ ~C 5 Comm, Simp
8.    C 6, 2, MP
9.    ~C ∨ M 7, Comm

10. ~~C

 8, DN
11.   M 9, 10 DS