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Exercise 8.6, III
59
(9) 1. (x)[Mx (y)(Py • Syx)]
9. (y)[(Py • Sym) (Py • Bym)] AIP
(10) 1. (x){Ix [(y)(Cy • Ay) Ex]}
2. [(x)Tx (x)Wx] [(x)Ix • (x)Cx]
Exercise 8.7
Part I.
Simple identity statements:
1. s = g
Statements involving "only," "the only," and "no except":
5. Wp • (x)(Wx x = p)
Superlative statements:
12. Eh • (x)[(Ex • x h) Lhx]
Statements involving "all except":
16. Ci • Si • (x)[(Cx • x i) Sx]
Exercise 8.7, I
Numerical statements:
20. (x)(y)[(Cx • Bx • Cy • By) x = y]
Statements containing definite descriptions:
30. (x)[Wxv • (y)(Wyv y = x) • Bx]
Assorted statements:
35. Sr • (x)[(Sx • x r) Srx]
45. (x){Ex • Dxn • (y)[(Ey • Dyn) y = x] • x = a}
Part II
(1) 1. (x)(x = a)
(2) 1. Ke
6. e n 3-5, IP
(3) 1. (x)(x = c Nx) / Nc
(4) 1. (x)(x = g)
(5) 1. (x)(Gx x = a)
9. Ha 6, 8, Id
(6) 1. (x)(Ax Bx)
2. Ac • Bi / c i
(7) 1. (x)(x = a)
Exercise 8.7, II
(8) 1. (x)(x = r)
10. Hn • Kr 6, 9, Conj
(9) 1. (x)(Lx x = e)
(10) 1. (x)(Px x = a)
4. Px ACP
(11) 1. (x)(y)(Txy x = e)
(12) 1. (x)[Rx (Hx • x = m)] / Rc Hm
(13) 1. (x)(Ba x a)
(14) 1. (x)Gx (x)(Kx • x = i) / Gn Ki
(15) 1. (x)(Rax Rxc)
(16) 1. (x)[Nx (Px • x = m)]
Exercise 8.7, II
11. Ne 3-10, IP
(17) 1. (x)(Fx x = e)
(18) 1. (x)[Ex (Hp • x = e)]
14. He 11, 13, Id
(20) 1. (x)[Fx (Gx • x = n)]
2. Gn (x)(Hx • x = e) / Fm He
Part III.
(1) 1. (x)(Nx • Wjx • Ix)
(2) 1. Ur • (x)[(Ux • x r) Orx]
Exercise 8.7, III
(3) 1. (x){Ax • Pxm • (y)[(Ay • Pym) y = x] • Fx}
(4) 1. (x){Nx • Tx • (y)[(Ny • Ty) y = x] • Wmx}
(5) 1. (x)[Wxk • (y)(Wyk y = x) • Ex • Ax]
14. Am 13, Simp
Exercise 8.7, III
(6) 1. (x){(Dx • Bx) • (y)[(Dy • By) y = x] • Lx • Tx}
(7) 1. Me • Se • (x)[(Mx • x e) Sx]
(8) 1. Pa • Oa • (y)[(Py • Oy) y = a]
Exercise 8.7, III
(9) 1. (x){Mx • Tx • (y)[(My • y x) Hxy]}
14. Mc 9, Simp
15. c a Hac 13, 14, MP
16. Hac • Mc • Tc 9, Com
Exercise 8.7, III
(10) 1. Bw • (x)[(Bx • x w) Twx]
23. ( a w) 8-22, IP
(11) 1. (x)(y)(Px • Lx • Py • Ly • x y)
10. (x)(Px • Lx • Fx) 3, QN
Exercise 8.7, III
19. Pa • Fa • La 18, Com
(12) 1. Df • Bf • Dp • Bp • (x)[(Dx • Bx) (x = f x = p)]
6. (Dp • p f) Rp 5, UI
16. (y)[(Dy • By • Ry) y = p] AIP
25. Da • Ba 24, Simp
(13) 1. (x)(y)(Ax • Ox • Ay • Oy • x y)
10. Ab • Ob • a b • Aa • Oa 5, Com
Exercise 8.7, III
39. (z)[(Pz • Oz) z = a z = b)] 20-38, IP
(14) 1. (x)(y)(z)[(Sx • Lx • Sy • Ly • Sz • Lz) (x = y x = z y = z)]
9. Sn • Cn • Ln AIP
22. Ra 21, Simp
(15) 1. Cm • Em • (x)[(Cx • x m) Ex]
(16) 1. Sc • Pc • Sn • Pn • (x)[(Sx • x c • x n) Px]
23. (y)[(Sy • Ry) y = c] AIP
40. (Sa • a c) (a n Pa) 39, Exp
55. (y)[(Sy • Ry) y = c] 23-54, IP
