- D. van Dalen. "Logic and Structures", Third Edition. Springer-Verlag, 1994. ISBN 0-387-57839-0 paperback.
- G.S. Boolos and R.C. Jeffrey. "Computability and Logic", Third Edition. Cambridge University Press, 1989. ISBN 0-521-38923-2 paperback.

- Propositional Logic: Propositions and Connectives, Semantics, Natural Deduction, Completeness.
- Predicate Logic: Quantifiers, Structures, Semantics, Natural Deduction, The Completeness Theorem, Compactness and Skolem-Löwenheim Theorems, Skolem Functions.
- Undecidability and Incompleteness: Turing Machines, Undecidability of
Predicate Logic, Gödel's First and Second Incompleteness Theorems.

### Homework Due in Class Wednesday, February 2

- Let
*n*and*k*be two distinct natural numbers. Prove that there is no 1-1 correspondence between a set with*n*elements and the set with*k*elements. - Prove that there is no 1-1 correspondence between a finite set and an
infinite set.
- Relying on the 1-1 correspondence between N and the set of non-negative
rationals shown in class, describe a 1-1 correspondence between N and Q.
- van Dalen, Exercises 2.2, p. 58: # 1 all, 2.
- van Dalen, Exercises 2.3, pp. 65-66: # 1, 2, 3, and 4.

- Let
### Homework Due in Class

- van Dalen, Exercises 2.5, pp. 78-79: # 9, 10, 12, 14, and 15
- van Dalen, Exercises 2.6, p. 80: # 2, 3, and 4.
- van Dalen, Exercises 2.7, pp. 88-89: # 6, 11, and 13.
- van Dalen, Exercises 1.4, pp. 38-39: # 1e, 2a, 3e, 4 both, and 5.
- van Dalen, Exercises 2.8, pp. 94-95: # 1 (ii) and 1 (vii) where x is not
free in phi.

- van Dalen, Exercises 2.5, pp. 78-79: # 9, 10, 12, 14, and 15

- Prove that the square root of 2 is not rational.
- van Dalen, Exercises 2.7, pp. 88-89: # 10 and 12.
- van Dalen, Exercises 3.2, pp. 117-118: # 6, 7, 8, 9, 10,
12, 13, 16, and 17.

- van Dalen, Exercises 3.3, pp. 132-136: # 5, 10, 11, 12, 15, 17, 18, 19,
20, 26, 27, 28(iii).
- van Dalen, Exercises 3.4, pp. 142-143: # 3, 4.
- Boolos and Jeffrey, Exercise 6.1, p. 66.
- Boolos and Jeffrey, Exercise 14.1. p. 168.
- Boolos and Jeffrey, Exercise 15.1, p. 180.
- Boolos and Jeffrey, Exercises 16.4 and 16.6, p. 190.