Exercise 8.2, III
35. (Hx • Mx) Kx 34, Simp
“The question of infants and mentally challenged adults raises an interesting point,” Paul
says. “I think what it comes down to is this. Something is considered to have rights if and only
[Note: This passage contains two arguments.]
1. (x)(Rx Lx)
“That sounds awfully arbitrary,” says Mindy. “But I think what it really comes down to
is power. Something is considered to have rights if and only if it has as much power as humans.
Animals do not have as much power as humans, so animals are not considered to have rights.
But that seems terribly wrong to me. It shouldn’t be a question of power. Anyway, now that our
food has arrived, how’s your steak?”
1. (x)(Rx Px)
Exercise 8.3
Part I
(1) 1. (x)Ax (x)Bx
(2) 1. (x)Ax (x)Bx
(3) 1. (x)Ax / (x)(Ax Bx)
(4) 1. (x)Ax (x)(Bx • Cx)
(5) 1. (x)(Ax • Bx) (x)(Cx • Dx)
Exercise 8.3, I
(6) 1. (x)Ax (x)(Bx Cx)
7. (x)Ax 6, EG
(7) 1. (x)(Ax Bx)
(8) 1. (x)Ax (x)Bx
Exercise 8.3, I
(9) 1. (x)(Ax Bx) (x)Cx
2. (x)Cx / (x)Ax
(10) 1. (x)(Ax • Bx)
2. (x)(Bx • Cx) / (x)(Ax Cx)
(11) 1. (x)(Ax • Bx)
2. (x)(Ax • Cx) / (x)[Ax (Bx • Cx)]
(12) 1. (x)[(Ax • Bx) Cx]
Exercise 8.3, I
8. (Am • Bm) Cm 1, UI
(13) 1. (x)(Ax • Bx) (x)Cx
7. (x)Cx 6, UG
(14) 1. (x)Ax (x)Bx
(15) 1. (x)(Ax Bx)
2. (x)Cx (x)Ax
9. Bx 8, Simp
(16) 1 (x)(Ax • Bx) (x)(Cx • Dx)
9. (x)(Cx • Dx) 8, EG
Exercise 8.3, I
16. (Ax Ex) • (Bx Fx) 15, DN
(17) 1. (x)(Ax • Bx) (x)(Cx Dx)
12. (Ax • Bx) 11, DM
(18) 1. (x)Ax [(x)Bx (x)Cx]
(19) 1. (x)(Ax • Bx) (x)(Bx Cx)
7. (x)(Bx Cx) 6, QN
(20) 1. (x)Ax (x)(Bx • Ax)
10. An 3, DN
Part II
(1) 1. (x)[Px (Hx Nx)] (x)Cx
Exercise 8.3, II
11. Pm 10, DN
(2) 1. Ia (x)(Px Ix)
(3) 1. (x)(Sx • Ax) (x)(Px • Rx)
2. (x)(Px Rx) / (x)(Sx Ax)
(4) 1. (x)(Gx • Px) (x)(Sx • Ex)
10. (x)(Sx • Ex) (x)(Gx • Px) 1, Com
(5) 1. (x)[(Px • Ax) Ix]
6. Ix Px 5, Com
7. Ix Px 6, Impl
(6) 1. (x)(Ix • Px)
7. Ix Px 5, DM
(7) 1. (x)(Px Sx) • (x)(Ix Gx)
Exercise 8.3, II
8. (x)(Ix Gx) 7, Simp
(8) 1. (x)(Ox • Gx) (x)(Hx • Rx)
2. (x)(Hx Gx) / (x)Ox
13. (Ox • Gx) 12, UI
(9) 1. (x){[(Ax Dx) • Px] (Ux • Sx)}
12. Px Dx 11, Simp
(10) 1. (x)[Px • (Gx Hx)]
9. Px Gx 8, Simp
18. (x)(Px • Nx) 17, UG
26. Pm 25, DN
Exercise 8.4
Part I
(1) 1. (x)(Ax Bx)
Exercise 8.4, I
(2) 1. (x)Ax (x)(Bx • Cx)
(3) 1. (x)Ax (x)(Bx • Cx)
(4) 1. (x)(Ax Cx)
Exercise 8.4, I
(5) 1. (x)(Ax Bx)
(6) 1. (x)Ax (x)Bx
(7) 1. (x)[(Ax Bx) Cx]
(8) 1. (x)(Ax Bx) (x)Ax / (x)Ax
2. (x)Ax AIP
(9) 1. (x)(Ax Bx)
(10) 1. (x)(Ax Bx)
2. Am An / (x)Bx
(11) 1. (x)[(Ax Bx) Cx]
2. (x)[(Cx Dx) Ax] / (x)Ax
Exercise 8.4, I
(12) 1. (x)Ax (x)(Bx Cx)
2. (x)Dx (x)Cx / (x)[(Ax • Dx) Bx]
(13) 1. (x)Ax (x)(Bx Cx)
2. (x)Dx (x)Bx / (x)(Ax • Dx) (x)Cx
(14) 1. (x)Ax (x)(Bx • Cx)
11. Bm • Cm 10, EI
Exercise 8.4, I
17. (x)Cx 16, DN
(15) 1. (x)Ax (x)(Bx • Cx)
(16) 1. (x)[(Ax Bx) Cx]
(17) 1. (x)Ax (x)(Bx • Cx)
2. (x)(Cx Bx) / (x)Ax (x)Cx
11. (x)Ax (x)Cx 4-10, CP
(18) 1. (x)(Ax Bx)
2. (x)[Ax (Bx Cx)]
(19) 1. (x)[Bx (Cx • Dx)] / (x)(Ax Bx) (x)(Ax Dx)
Exercise 8.4, I
(20) 1. (x)[Ax (Bx • Cx)]
(22) 1. (x)Ax (x)Bx / (x)(Ax Bx)
Exercise 8.4, I
6. An 5, Simp
(23) 1. (x)(Ax Ex) (x)(Bx • Cx)
9. Bx 8, Simp
(24) 1. (x)(Ax Bx)