Symbolic Logic, Dale Jacquette, Wadsworth, 2001, Chapter 8, Exercise IV, problem 5

We are asked here to symbolize the argument, verify the translation by the truth tree method, and give a natural deduction proof. I don't know how to do a truth tree using blogger tools - I can just about do it in Word, with a little patience, so only the translation and the deduction follow.

Everything is either an unconscious or immaterial entity. All sentient beings, if they are physically embodied, are material entities. Hence, no sentient, physically embodied beings are conscious.

Using the glossary provided (C, M, E, S, B, P), we get:

1. (x)[Ex ⊃(¬ Cx ∨ ¬ Mx)]
2. (x){(Sx • Bx) ⊃[Px ⊃ (Mx • Ex)]
3. ∴(x)[Sx • Px • Bx) ⊃¬ Cx]
4. * Sx • Px • Bx ......... ACP
5. * (Sx • Bx) ⊃[Px ⊃ (Mx • Ex)] ......... 2UI x/x
6. * Sx • Bx ......... 4Simp.
7. * Px ⊃ (Mx • Ex) ......... 6,5MP
8. * Px ......... 4Simp.
9. * Mx • Ex ......... 8,7MP
10. * Mx ......... 9Simp.
11. * Ex ......... 9Simp.
12. * Ex ⊃(¬ Cx ∨ ¬ Mx) ......... 1UI x/x
13. * ¬ Cx ∨ ¬ Mx ......... 11,12MP
14. * ¬ Cx ......... 10,13DS
15. Sx • Px • Bx) ⊃¬ Cx ......... 4-14CP
16. (x)[Sx • Px • Bx) ⊃¬ Cx] ......... 15UG