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Lab 1 Chapter 1, Sections 1.1, 1.2, 1.3, and 1.4 Book: Discrete Mathematics and Its Applications By Kenneth H. Rosen 1.1 Page 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”? 1.1 Page 20, Exercise 55 A says “At least one of us is a knave” and B says nothing. 1.1 Page 19, Exercise 29, e Construct the truth table for the following compound proposition. (p q) (p r) 1.1 Page 19, Exercise 38, b Evaluate each of the expression. (0111110101)01000 1.2 Page 26, Example 7 Show that (p(pq)) and pq are logically equivalent. 1.2 Page 28, Exercise 10, c Using Truth tables show that the following is a tautology [p(pq)]q 1.2 Page 28, Exercise 11, f from 9 Without using Truth tables show that the following is a tautology (pq)q 1.3 Page 39, Example 19 Show that x(P(x)Q(x)) and xP(x) xQ(x) are logically equivalent. 1.3 Page 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) 1.3 Page 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) 1.3 Page 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) 1.4 Page 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? yxQ( x, y) xyQ( x, y) 1.4 Page 61, Exercise 32, d Express the negations of each of these statements so that all negation symbols immediately precede predicates. yxz (T ( x, y, z ) Q( x, y)) 1.1 Page 21, Exercise 65 • Five men with different nationalities and with Five men with different nationalities and with different different live in consecutive onThe a houses jobs live injobs consecutive houses onhouses a street. street. The different houses are painted colors. Thepets are painted colors. The different men have different menhave havedifferent differentfavorite pets and haveDetermine different favorite and drinks. drinks. Determine who owns a zebra and whose favorite drink is mineral who owns zebra whose favorite drink is water (whicha is one and of the favorite drinks) mineral water (which is one of the favorite drinks) given these clues1: given these clues1: 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. Blue Green Red White Yellow Blue Green Red White Yellow Blue Green Red White Yellow Blue Green Red White Yellow Blue Green Red White Yellow Englishman Italian Japanese Norwegian Spaniard Englishman Italian Japanese Norwegian Spaniard Englishman Italian Japanese Norwegian Spaniard Englishman Italian Japanese Norwegian Spaniard Englishman Italian Japanese Norwegian Spaniard Job Diplomat Painter Photographer Physician Violinist Diplomat Painter Photographer Physician Violinist Diplomat Painter Photographer Physician Violinist Diplomat Painter Photographer Physician Violinist Diplomat Painter Photographer Physician Violinist Pet Dog Fox Horse Snails Zebra Dog Fox Horse Snails Zebra Dog Fox Horse Snails Zebra Dog Fox Horse Snails Zebra Dog Fox Horse Snails Zebra Coffee Milk Orange Juice Tea Mineral Water Coffee Milk Orange Juice Tea Mineral Water Coffee Milk Orange Juice Tea Mineral Water Coffee Milk Orange Juice Tea Mineral Water Coffee Milk Orange Juice Tea Mineral Water 1 2 3 4 5 color Nationality Drink House