Introductory Logic
Quiz #10
December 2, 2005
 

Name______________________
R. Hammack
Score _________
DIRECTIONS. Use new rules UI, EI, UG, EG, CQ with the 18 rules of inference to deduce the conclusions of the following arguments.

1.

1.     (x)(Ax ⊃ Bx)  
2.     (x)(Bx ⊃ Cx) /     (x)(Ax ⊃ Cx)
3.     Ay ⊃ By 1, UI
4.     By ⊃ Cy 2, UI
5.     Ay ⊃ Cy 3, 4, HS
6.     (x)(Ax ⊃ Cx) 5, UG



2.

1.     (∃x)~Bx  ⊃  (x)(Cx ⊃ Dx)  
2.     ~(x)(Bx ∨ Dx) /    ~(x)Cx
3.     (∃x)~(Bx ∨ Dx) 2, CQ
4.     ~(Ba ∨ Da) 3, EI
5.     ~Ba • ~Da 4, DM
6.     ~Ba 5, Simp
7.     (∃x)~Bx 6, EG
8.     (x)(Cx ⊃ Dx) 1, 7, MP
9.     Ca ⊃ Da 8, UI
10.    ~Da 5, Comm, Simp
11.    ~Ca 9, MT
12.    (∃x)~Cx 11, EG
13.    ~(x)Cx 12, CQ