Chapter 2: Hints and Selected Solutions
Section 2.1 (page 44)
2.1 Sound in Socrates World? Yes Sound in Wittgensteins World? No
Argument 1. 2. 3. 4. 5. 6. 7. 8. 2.2 1.
Valid? Yes
Yes
Yes
No
No
No
No
Anyone who wins an academy award is famou
Chapter 3: Hints and Selected Solutions
Section 3.1 (page 70)
3.2 1. True 4. To see why this sentence is false, you may need to switch to the 2D view, since the label f is barely visible in the 3D view. 5. This is false since it claims that a and b
Chapter 4: Hints and Selected Solutions
Section 4.1 (page 104)
4.2 1. The truth table for (A B) (A B) is shown in Figure ?. Since all the entries under the main connective () are T, it shows that the sentence is a tautology.
4.5 The truth table
Chapter 5: Hints and Selected Solutions
Section 5.1 (page 131)
5.1 The pattern From P Q and P, infer Q is valid. If P Q is true, then by the truth table for , at least one of P or Q must be true. But if P is true, then by the truth table for, P mu
Chapter 6: Hints and Selected Solutions
Section 6.2 (page 154)
6.2
6.4
1
6.9
Section 6.3 (page 161)
6.10 One of many possible counterexamples to the following argument is shown below. Cube(a) Cube(b) (Cube(c) Cube(b) Cube(c) You should turn in
Chapter 7: Hints and Selected Solutions
Section 7.2 (page 183)
7.2 The truth table for this Exercise is shown below. Since all the entries in the main columns for each sentence are the same, row by row, the sentences are tautologically equivalent.
Chapter 8: Hints and Selected Solutions
Section 8.1 (page 203)
8.1 1. Arming the consequent is invalid. 4. Weakening the Antecedent invalid. 7. Constructive Dilemma is valid. 8.4 Here is an informal proof of the argument: The unicorn, if horned, is
Chapter 9: Hints and Selected Solutions
Section 9.3 (page 234)
9.1 The rst four sentences:
9.2 Here is one possible way of xing up the odd numbered sentences:
1
Section 9.4 (page 238)
9.7 According to the formation rules, quantiers can combine wi
Chapter 10: Hints and Selected Solutions
Section 10.1 (page 264)
10.1 The following lls in some of the rows for you. Be sure you understand these. Annotated sentence Truth-functional form 1. 4. 7. 10 x (x = x)A x (Cube(x) Small(x)A x (Small(x) Cu
Chapter 11: Hints and Selected Solutions
Section 11.1 (page 291)
11.4 1. xy [(Small(x) Large(y) FrontOf(x, y) 4. xy (Tet(x) Tet(y) SameCol(x, y) 7. xy (Tet(x) Tet(y) x = y SameSize(x, y) 11.7 2. Some of the parties are not lonely. 4. There is
Chapter 12: Hints and Selected Solutions
Section 12.3 (page 327)
12.1 The argument is valid and the proof is a good one. In the following, we repeat the proof, but being explicit about the proof methods being used. x [(Brillig(x) Tove(x) (Mimsy(x)
Chapter 13: Hints and Selected Solutions
Section 13.1 (page 346)
13.2 Hint (ll in the supports):
13.7 Hint:
1
Section 13.2 (page 350)
13.11 A counterexample:
13.14 Hint:
2
Section 13.3 (page 337)
13.20 The following proof formalizes the inform
Chapter 14: Hints and Selected Solutions
Section 14.1 (page 371)
14.1 One way to do the You Try It is shown in the two worlds below. You should submit dierent looking worlds.
1
14.2
1. There is exactly one tove. 4. All toves are identical (=). 1.
Chapter 15: Hints and Selected Solutions
Section 15.1 (page 411)
15.1 Hint: The exercise is to test your understanding of the axiom of extensionality. According to that axiom, sets are identical if and only if they have the same members, regardless
Chapter 16: Hints and Selected Solutions
Section 16.1 (page 449)
16.3 You are asked to give two distinct derivations of the ambig-w A1 A2 A2 . Here is one. You should be able to think of another. By the basis clause, A2is an ambig-w. Hence, by the
Chapter 17: Hints and Selected Solutions
Section 17.1 (page 470)
17.1 Here for your convenience is the truth table (P, Q, R): P t t t t f f f f Q t t f f t t f f R t f t f t f t f (P, Q, R)
T T F F T F T F
This can be nicely captured as follows: h
Chapter 18: Hints and Selected Solutions
Section 18.1 (page 498)
18.2 1. This is an allowable change. The language in question does not have any position predicates, so the model for the original world and the modied world are identical. 4. If we ma
Chapter 19: Hints and Selected Solutions
Section 19.2 (page 531)
19.1 1. cLarger(a,x) has date of birth = 1. This constant is also called c1 later in the exercise. 2. cLarger(c1 ,x) has date of birth = 2. This constant is also called c2 later in the