Lab 1 Chapter 1, Sections 1.1, 1.2, 1.3, and 1.4

1. Lab 1Chapter 1, Sections 1.1, 1.2, 1.3, and 1.4 Book: Discrete Mathematics and Its Applications By Kenneth H. Rosen

2. 1.1Page 13, Example 18 • An Island that has two kinds of inhabitants, knights, who always tell the truth, and their opposites, knaves, who always lie. You encounter two people A and B. What are A and B if A says “B is a knight” and B says “The two of us are opposite types”?

3. 1.1Page 20, Exercise 55 • A says “At least one of us is a knave” and B says nothing.

4. 1.1Page 19, Exercise 29, e • Construct the truth table for the following compound proposition. • (p  q) (p  r)

5. 1.1Page 19, Exercise 38, b • Evaluate each of the expression. • (0111110101)01000

6. 1.2Page 26, Example 7 • Show that (p(pq)) and pq are logically equivalent.

7. 1.2Page 28, Exercise 10, c • Using Truth tables show that the following is a tautology [p(pq)]q

8. 1.2Page 28, Exercise 11, f from 9 • Without using Truth tables show that the following is a tautology (pq)q

9. 1.3Page 39, Example 19 • Show that x(P(x)Q(x)) and xP(x) xQ(x) are logically equivalent.

10. 1.3Page 45, Example 27 • “All hummingbirds are highly colored” • “No large birds live on honey” • “Birds that do not live on honey are dull in color” • “Hummingbirds are small” • Let P(x),Q(x),R(x), and S(x) be the statements “x is a hummingbird”, “x is large”, “x lives on honey”, and “x is richly colored” • Domain: all birds • Express the statement in the argument using quantifiers and P(x), Q(x), R(x), and S(x)

11. 1.3Page 45, Example 28 Instructor(chan, math273) Instructor(patel,ee222) Instructor(grossman,cs301) Enrolled(kevin,math273) Enrolled(juana,ee222) Enrolled(juana,cs301) Enrolled(kiko,math273) Ernolled(kiko,cs301) Teaches(p,s):- instructor(P,C), enrolled(S,C) • ?Enrolled(kevin, math) • ?enrolled(x,math273) • ?teaches(x,juna)

12. 1.3Page 50, Exercise 55, c Instructor(chan, math273) Instructor(patel,ee222) Instructor(grossman,cs301) Enrolled(kevin,math273) Enrolled(juana,ee222) Enrolled(juana,cs301) Enrolled(kiko,math273) Ernolled(kiko,cs301) Teaches(p,s):- instructor(P,C), enrolled(S,C) • ?enrolled(X,CS301)

13. 1.4Page 61, Exercise 26, g, f Let Q(x,y) be the statement “x+y=x-y.” if the domain for both variables consists of all integers, what are the truth values?

14. 1.4Page 61, Exercise 32, d • Express the negations of each of these statements so that all negation symbols immediately precede predicates.

15. Five men with different nationalities and with different jobs live in consecutive houses on a street. The houses are painted different colors. The men have different pets and have different favorite drinks. Determinewho owns a zebra and whose favorite drink is mineral water (which is one of the favorite drinks)given these clues1: 1.1 Page 21, Exercise 65 • Five men with different nationalities and with different jobs live in consecutive houses on a street. The houses are painted different colors. The men have different pets and have different favorite drinks. Determinewho owns a zebra and whose favorite drink is mineral water (which is one of the favorite drinks)given these clues1:

16. 1.1 Page 21, Exercise 65 1. The Englishman lives in the red house. 2. The Spaniard owns a dog. 3. The Japanese man is a painter. 4. The Italian drinks tea. 5. The Norwegian lives in the first house on the left. 6. The green house is on the right of the white one. 7. The photographer breeds snails. 8. The diplomat lives in the yellow house. 9. Milk is drunk in the middle house. 10. The owner of the green house drinks coffee. 11. The Norwegian’s house is next to the blue one. 12. The violinist drinks orange juice. 13. The fox is in a house next to that of the physician. 14. The horse is in a house next to that of the diplomat.