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Discrete Structures, Logic, and Computability, 4th Edition by James L. Hein

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Chapter 2

Section 2.1

1. a. There is one function of type {a, b} → {1}; it maps both a and b to 1.c. There are four functions of type {a, b} → {1, 2}: one maps both a and b to 1; one maps both a and b to 2; one maps a to 1 and b to 2; and one maps a to 2 and b to 1.

2. a. O. c. {x | x = 4k + 3 where kN}. e. ∅.

3. a. E. c. E – {0}. d. N.

4. a. −5. c. 4.

6. For example, x = y = ½.

7. a. 3. c. 1.

8. a. 1. b. 2. c. 3.

9. gcd(296, 872) = 8 = (−53) · 296 + 18 · 872.

10. a. 3. c. 3.

11. {0, 1, 2, 3, 4, 5, 6}.

12. a. f (∅) = ∅ c. f ({2, 5}) = {4}. e. f ({1, 2, 3}) = {0, 2, 4}.

13. a. 11001. c. 1101111.

14. a. 43. c. 2127.

15. a. floor(x) = if x ≥ 0 then trunc(x) else if x = trunc(x) then x else trunc(x − 1).

16. When x is negative, f(x, y) can be ...

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