Introductory Logic
Quiz #8
May 10, 2006
 

Name______________________
R. Hammack
Score _________

Deduce the conclsions of the following arguments. You may use any of 25 rules as well as indirect and conditional proof.

1. 1.     (∃x)(Ax • Bx)  ⊃  (x)Mx  
2.     ~Md /    (x)(Ax ⊃ ~Bx)
3.     (∃x)~Mx 2, EG
4.     ~(x)Mx 3, CQ
5.     ~(∃x)(Ax • Bx)  1, 4, MT
6.     (x)~(Ax • Bx)  5, CQ
7.     (x)(~Ax ∨ ~Bx)  6, DM
8.     (x)(Ax ⊃ ~Bx) 7, Impl
   




2. 1.     (x)~Bx  ⊃  (∃x)Ax  
2.     (x)(Ax ⊃ Bx) /    (∃x)Bx
  3.     ~(∃x)Bx AIP
  4.     (x)~Bx 3 CQ
  5.     (∃x)Ax 1, 4, MP
  6.     Am 5, EI
  7.     Am ⊃ Bm 2, UI
  8.     Bm 6, 7, MP
9.     ~Bm 4, UI
10.     Bm • ~Bm 8, 9 conj
11.     (∃x)Bx 3-10 IP