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.
 (0111110101)01000

1.2
Page 26, Example 7

Show that (p(pq)) and pq are
logically equivalent.
1.2
Page 28, Exercise 10, c
Using Truth tables show that the following
is a tautology
[p(pq)]q

1.2
Page 28, Exercise 11, f from 9
Without using Truth tables show that the
following is a tautology
(pq)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?
yxQ( x, y)
xyQ( 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.
yxz (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