Introductory Logic
Quiz #7
May 1, 2006
 

Name______________________
R. Hammack
Score _________

1. Translate the following statements into symbolic form.


(a)
     A student went on the trip.    (S, T)
    (∃x)(Sx • Tx)


(b)
     Any well-made car runs smoothly.    (W, C, R)
    (x)((Wx • Cx)  ⊃  Sx)


(c)
     If any witnesses told the truth, then either Parsons or Harris is guilty.    (W, T, G)
    (∃x)(Wx • Tx)  ⊃  (Gp ∨ Gh)




2. Use new rules UI, EI, UG, and EG with the 18 rules of inference to deduce the conclusion of the following argument.

1.     (∃x)Ax  ⊃  (x)(Bx ⊃ Cx)  
2.     Am • Bm /    (∃x)(Ax • Cx)
3.     Am 2, Simp
4.     Bm 2, Comm, Simp
5.     (∃x)Ax 3, EG
6.     (x)(Bx ⊃ Cx) 1, 5, MP
7.     Bm ⊃ Cm 5, UI
8.     Cm 7, 4, MP
9.     Am • Cm 3, 8, Conj
10.  (∃x)(Ax • Cx) 9, EG