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Assignment #2
Due Tuesday, 1/27
Complete the following exercises from chapter 1.3:
2, 8, 10
Complete the following exercises from chapter 1.4:
d
14, 28, 32(a,b, and d)
Complete the following exercises from chapter 1.5:
14, 24
For question 14, translate the arguments to mathematical symbols and do twocolumn proofs in the style of examples
12 and 13 on page 71
Points assigned
1.4.14 gets 20 points
1.5.14 gets 20 points
Each remaining problem gets 10 points
Chapter 1.3 Exercise 2:
Let P(x) be the statement “the word
x
contains the letter a.”
What are the truth values for the following?
Chapter 1.3 Exercise 8:
Translate these statements into English, where R(x) is “x is a rabbit” and H(x) is “x hops” and the domain
consists of all animals.
a)
2200
x(R(x)
H(x))
b)
2200
x(R(x)
∧
H(x))
c)
5
x(R(x)
H(x))
d)
5
x(R(x)
∧
H(x))
Part
Statement
truth value
a
P(orange)
T
b
P(lemon)
F
c
P(true)
F
d
P(false)
T
Part
Statement
English Sentence
a
2200
x(R(x)
H(x))
If an animal is a rabbit, then that animal hops.
Alternatively, every rabbit hops.
b
2200
x(R(x)
∧
H(x))
Every animal is a rabbit and hops.
Alternatively, every animal is hopping rabbit.
Alternatively, every animal is a rabbit that hops.
c
5
x(R(x)
H(x))
There exists an animal such that if it is a rabbit, then it hops.
d
5
x(R(x)
∧
H(x))
There exists an animal that is a rabbit and hops.
Alternatively, some rabbits hop.
Alternatively, some hopping animals are rabbits.
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View Full DocumentChapter 1.3 Exercise 10:
Let C(x) be the statement “x has a cat,” D(x) be the statement “x has a dog,” and F(x) be the statement “x
has a ferret.” Express each of these statements in terms of C(x), D(x), and F(x), quantifiers, and logical
connectives. Let the domain consist of all students in your class.
Chapter 1.4 Exercise 14: 20 points
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 Spring '09

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