About the Book

New Exercises

Logic in Action

Software

Additions and Changes

Errata

Above and Beyond

Slide the Symbols

About the Author

Acknowledgments

 

Comments on the Book

Comments on this site

 

 

1. (x) (P¹x L²xr)
2. (x) (L²jx) v (y (F²jy)
3. (x) (P¹x & S²jx)
4. (x) (M¹x & S²dx)
5. (x) (S¹x T³axt)

B.

#1.

1. (x) (B¹x H²rx)
2. B¹f
3. H²rf

#2.

1. (x) (C¹x & B³nxr)
2. (x) (C¹x & H²rx)

#3.

1. K³ceb
2. (x) (P¹x & K³cxb) & (y) (P¹y & K³yeb)

Chapter 13

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A.

1. (x) (P¹x & (y) (P¹y L²xy))
2. (x) (P¹x & (y) (P¹y L²yx))
3. (x) (M¹x & (y) (B¹y (z) (L¹z P³yzx)))
4. (x) (G¹x & ~(y) (B¹y & (z) (P¹z P³xyz)))
5. (x) (D¹x (y) (S¹y & (z) (P¹z & W³yxz)))
6. (x) (B¹x & (y) (S¹y & (z) (T¹z R³yxz)))
7. (x) (C¹x & y) (P¹y z) (D¹z S³yxz)))

B.

#1.

1. (x) (L¹x (y) (F¹y & (z) (T¹z & P³xyz)))
2. (x) (L¹x)
3. (x) (F¹x & (y) (T¹y & (z) (L¹z & P³zxy)))

#2.

1. (x) (P¹x & (y)) (T¹y (z) (F¹z & E³xzy)))
2. (x)) (T¹x (y) (F¹y & (z) (P¹z & E³zyx)))

#3.

1. (x) (T¹x & (y) (C¹y (z) (G¹z & ~C³yxz))) (This sentence is ambiguous; if you think the sentence can be true if one or two cats climb the tree -- as long as not ALL cats do so -- then you might be inclined to symbolize it as follows: (x) (T¹x & ~(y) (C¹y (z) (G¹z & C³yxz))) )
2. (x) (C¹x (y) (G¹y & (z) (T¹z & C³xzy)))

#4.

1. (x) (L¹x (y) (T¹y & (z) (W¹z L³yxz)))
2. (x) (L¹x)
3. (x) (L¹x & (y) (W¹y (z) (T¹z & C³zxy)))

Chapter 14

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A.

#1.

	1.	(x) (B1x H2rx)	P
	2.	B1f	P
	3.	~H2rf	NC
X	4.	B1f H2rf	1, UQ
	5.	/ \ ~B1f H2rf X X	4,

All branches close: valid argument.

#2.

X	1.	(x) (C1x & B3nxr)	P
X	2.	~(x) (C1x & H2rx)	NC
	3.	(x) ~ (C1x & H2rx)	2, QE
X	4.	C1a & B3nar	1, EQ
X	5.	~ (C1a & H2ra)	3, UQ
	6.	C1a	4, &
	7.	B3nar
	8.	/ \ ~C1a ~H2ra X O	5, ~&

Open branch: invalid argument

Chapter 15

Top

A.

1. ~(x) (P¹x & (y) (T¹y H²xy))
2. ~(x) (P¹x & ~(y) (T¹y & H²xy))
3. (x) (C¹x & (y) (G¹y ~E²xy))
4. (x) (C¹x ~(y) (G¹y & E²xy))

B.

#1.

1. (x) (H¹x (y) (P¹y & ~(z) (N¹z & C³xyz)))
2. (x) (H¹x A¹x)
3. ~( (x) (A¹x (y) (P¹y & (z) (P¹z & C³xyz))))

#2.

1. ~(x) (D¹x & B¹x)
2. (x) (D¹x v A¹x)
3. (x) (P¹x & ~A¹x)
4. ~(~(x) (P¹x & ~B¹x))

C.

1. (x) ( (y) (F¹y & H²xy) C¹x)
2. (x) ((y) (W¹y & B²xy) F¹x)
3. (x) (P¹x ((y) (B²xy A¹y))
4. ~((x) ((y) (S²xy B¹y ) S¹x)

D.

#1.

1. (x) ((y) (T¹y & C²xy) C¹x)
2. (x) ((y) (S¹y & A²xy) (z) (T¹z & C²xz))
3. (x) ((y) (S¹y & A²xy) C¹x)

#2.

1. (x) ((y) (L²xy L¹y) T¹x)
2. (x) (P¹x & (y) (B¹y & L²xy))
3. ~(x) (P¹x T¹x)

E.

#1

1. (x) (P¹x ((y) (C¹y (O²xy B²xy))))
2. (x) ((C¹x & (y) (P¹y & B²yx)) S¹x)
3. (x) ((C¹x & (y) (P¹y & B²yx)) S¹x)

#2.

1. (x) (B¹x ((y) (A¹y (M²xy R²xy))))
2. B¹s & A¹h
3. M²sh R²sh

#3.

1. (x) (P¹x ((y) (F¹y (S²xy K²xy))))
2. ~(x) (F¹x ((y) (P¹y (K²yx S²yx))))
3. (x) (P¹x & (y) (F¹y & S²xy & ~K²xy))

F.

#1-#4: see M&A solutions

#5.

1. (x) (C¹x ((y) (M¹y (C²xy E²xy))))
2. (x) ((y) (M¹y & E²xy) ~H¹x)
3. ~(x) (C¹x & (y) (M¹y & C²xy) & H¹x)

#6.

1. (x) ((P¹x & F¹x) (y) (P¹y L²yx))
2. (x) (P¹x (y) (P¹y & ~L²yx)
3. ~(x) (P¹x & F¹x)

#7.

1. ~(x) (P¹x & (y) (D¹y & P²xy) & U¹x)
2. ~(x) (P¹x (y) (D¹y & P²xy))
3. ~ (x) (P¹x (y) ((D¹y &P²xy) ~U¹x))

#8.

1. (S¹j (x) (B¹x P¹x)) & ((y) (B¹y P¹x) S¹j)
2. (x) (T¹x & M²jx) (x) (B¹x ~P¹x)
3. ~(x) (T¹x & M²jx) A¹j
4. ~A¹j ~S¹j

#9.

1. ~(x) (P¹x & (y) (T¹y (~S²xy & W²xy))
2. ~(x) (P¹x & (y) (T¹y ~W²xy) & (z) (C¹z W²xz))
3. (x) ((P¹x & (y) (C¹y W²xy)) (z) (T¹z S²xz))

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