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Chapters 16 & 17

Chapters: | 16 | 17 |

Chapter 16

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A.

#1.

1. (x) (B¹x R²hx)
2. h = a
3. (x) (B¹x R²ax)

#2.

1. (x) (D¹x P²cx)
2. c = d
3. (x) (D¹x P²dx)

B.

	1.	(x) (F2xa (B1x & C1x))			P
	2.	F2ba			P
X	3.	~(x) (B1x & C1x & x=b)			NC
	4.	(x) ~(B1x & C1x & x=b)			3, QE
X	5.	F2ba (B1b & C1b)			1, UQ
X	6.	/ \ ~F2ba (B1b & C1b) X |			5,
	7.		B1b		6, &
	8.		C1b
X	9.		~(B1b & C1b & b=b)		4, UQ
	10.		/ | \ ~B1b ~C1b ~b=b X X |		9, ~& twice
	11.		b=b X		I I

All branches closed: valid argument

C.

1. (x) (P¹x & (y) (P¹y & x y & H¹x & H¹y))
2. (x) (T¹x & D¹x (y) (T¹y & D¹y x = y))

D.

1. (x) (P¹x & L²xs & (y) ((P¹y & L²ys) x=y))
2. (x) (P¹x & (y) (C¹y E²xy) & (z) ((P¹x & (x₁) (C¹x₁ E²zx₁)) x₁ = z))

E.

#1.

1. (x) (M¹x & L²xl & (y) ((M¹y & L²yl) x = y) & L¹x)
2. (x) (M¹x & L¹x & (y) ((M¹y & L¹y) x=y)

#2.

1. (x) ((P¹x & E¹x) (y) ((P¹y & E¹y) (z)((P1z & E1z) (x = y v x=z v y=z))))
2. E¹n & E¹l
3. ~E¹m

#3.

1. (x) (H¹x & H²ax & (y) (H¹y & H²ay & xy))
2. (H¹c & H²ac) & (H¹k & H²ak)
3. c = k (x) (H¹x & H²ax & x c & xk)

Chapter 17

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A.

#1.

1. (x) (T²xc & I²xr & A²xt)
2. (x) (y) (P¹y & T²xy & A²xt)

#2.

1. (x) (K³xaj &A²xw)
2. (x) (y) (z) (P¹y & P¹z & K³xyz & A²xw)

B.

#1.

1. (x) (S²xm & B¹x) & (y) (A²ym & R¹y)
2. (x) (S²xm) & (y) (A²ym)

#2.

1. (x) (P²xr & H¹x) & (y) (W²yr & Q¹y)
2. ~(x) (P²xr & Q¹x)

#3.

1. (x) (P¹x & (y) (E²yx & (z) (D¹z O²yz)))
2. (x) (E²xa (O²xs v O²xw))
3. (x) (P¹x & (y) (E²yx) & xa)

C.

#1.

1. (x) (y) ((P¹y & T²xy & R¹x) (z) (P¹z & zy & (x₁) (M³x₁zy)))
2. (x) (T²xl & R¹x) (y) (P¹y & (z) (M³zyl))

#2.

1. (x) (y) (z) (A³xyz & B¹x) (x₁) (y₁) (P¹x₁ & C²y₁x₁)
2. (x) (y) (z) (A³xyz & L¹x) (x₁) (y₁) (P¹x₁ & L²y₁x₁ & H¹y₁)
3. (x) (A³xja) ((y) (z) (P¹y & C²zy) v (x₁) (y₁) (P¹x₁ & L²y₁x₁))

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