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Exercise 8.1, I
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Chapter 8
Exercise 8.1
Part I
1. Ce
2. Sn
7. (x)(Mx Tx)
14. (x)(Lx Wx)
20. (x)[(Cx • Mx) (Vx • Nx)]
26. (x)(Tx • Wx)
35. (x)[Ax (Sx Px)]
43. (x)[(Vx Cx) (Sx • Ix)]
50. (x)(Wx • Tx) (Gp Gh)
Exercise 8.2
Part I
(1) 1. (x)(Ax Bx)
(2) 1. (x)(Bx Cx)
(3) 1. (x)(Ax Bx)
(4) 1. (x)(Ax Bx)
(5) 1. (x)[Ax (Bx Cx)]
(6) 1. (x)[(Ax Bx) Cx]
(7) 1. (x)[Jx (Kx • Lx)]
(8) 1. (x)[Ax (Bx Cx)]
(9) 1. (x)(Ax Bx)
(10) 1. (x)(Ax Bx)
(11) 1. (x)(Bx Ax)
Exercise 8.2, I
(12) 1 (x)Ax (y)(By Ay)
(13) 1. (x)[(Ax • Bx) Cx]
2. (x)(Bx • Cx) / (x)Ax
13. (x)Ax 12, EG
(14) 1. (x)(Ax Bx)
(15) 1. (x)Ax (x)(Bx Cx)
2. Am • Bm / Cm
(16) 1. (x)Ax (x)Bx
2. (x)Cx (x)Dx
(17) 1. (x)(Ax • Bx)
2. Cr (x)Bx / (x)(Cx • Ax)
(18) 1. (x)[Ax (Bx Cx)]
Exercise 8.2, I
(19) 1. (x)Ax (x)(Cx Bx)
2. (x)(Ax Bx)
(20) 1. (x)Ax (x)(Bx Cx)
(21) 1. (x)(Ax • Bx) (x)(Cx • Dx)
2. (x)Ax (x)(Bx • Cx)
(22) 1. (x)(Ax • Bx)
2. An [(x)Cx Bc]
(23) 1. (x)(Ax • Bx)
Exercise 8.2, I
(24) 1. (x)Ax (x)[(Ax Ex) Dx]
(25) 1. (x)Ax (x)(Ax Bx)
Exercise 8.2, I
Part II
(1) 1. (x)(Ox Sx)
(2) 1. (x)(Tx Vx) / (x)[(Tx • Gx) Vx]
(3) 1. (x)[(Ax Px) Gx] / (x)(Ax Gx)
(4) 1. (x)(Cx Vx) • (x)(Px Fx)
6. (x)(Px • Gx) 5, Simp
(5) 1. (x)[(Bx Px) Lx]
12. (x)(Gx Bx) 11, UG
(6) 1. (x)(Cx • Gx)
Exercise 8.2, II
(7) 1. (x)[Gx (Ix • Px)]
(8) 1. (x)(Hx • Rx)
(9) 1. (x)(Rx • Wx) (x)(Cx Px)
2. (x)(Lx • Wx) (x)(Px Bx)
Exercise 8.2, II
12. Lm • Wm 6, 10, Conj
(10) 1. (x)[(Ax • Kx) Rx] (x)(Gx Sx)
Part III (The letters used in the translations are underlined in the text.)
Where’s the Beef?
“Have you decided what to order?” Paul says to Mindy, as he folds his menu and puts it on the
table.
“I think I’ll have the tofu stir-fry,” she replies. “And you?”
Exercise 8.2, III
Mindy smiles too. “First date,” she says.
“Yeah,” says Paul. “What made you decide to become a vegetarian?”
1. (x)[Mx (Ox • Ax)]
2. (x)(Ox Hx)
14. Mx Hx 9, 13, HS
24. (x)(Mx Lx) 23, UG
“I might add that if people who eat meat are less healthy, then if parents are responsible,
then they will refrain from feeding meat to children. All parents love their children, and if they
[Note: You must include the prior conclusion as a premise. Mx = x is a meat-
eater, Fx = x is a future meat-eater.]
1. (x)(Mx Lx)
5. (x)(Px Ex) (x)(Cx Gx)
9. Px Cx 3, UI
18. (Rx • Px) Ex 17, Com
“Well, I won’t hold my breath on that,” Paul says, as he offers Mindy a slice of bread
from the basket on the table. “If children and teenagers fail to eat meat, then they become
1. (x)[(Cx Tx) (Mx Zx)]
9. (Cx • Tx) (Mx Zx) 8, DM
22. [Cx • (Cx • Mx)] Wx 21, Com
34. Cx (Mx Lx) 33, Exp
35. Ex (Mx Ix) 4, UI
46. Ex (Bx Lx) 6, UI
65 (x)[(Cx Ex) (Mx Lx)] 64, UG
Exercise 8.2, III
Mindy smiles. “That’s what zinc tablets and iron supplements are for,” she says.
1. (x)(Ax Sx)
2. (x)(Ax Ix)
10. Hx [Kx (Cx Ex)] 5, UI
23. (Hx Mx) (Cx • Ex) 22, Dist
“I agree with you that animals should not be made to suffer,” Paul responds.
1. (x){Ax [Rx (Px Dx)]}
Exercise 8.2, III
“But,” Paul continues, “your argument also suggests that animals have rights. If animals
1. (x)[Ax (Rx Mx)]
8. Ax Sx 5, UI
19. Ax (Ax Rx) 18, DM
“Well,” Mindy replies, “by that line of reasoning infants and mentally challenged adults
1. (x)[(Ix Ex) Rx]
8. Rx (Ix Ex) 7, Com
16. (x)(Ax Rx) 3, 15, MP
27. Ax Lx 26, Trans
