Download Homework Chapter 1 - Mathematical Logic

Homework Chapter 1 - Mathematical Logic
1.1
1.3
1.4
1.6
11, 23a-d
11(just parts a, b and c in 9), 25, 32, 41
6, 25
9a,b,c, 23, 24
1. Write the negation of each of the following propositions without using any form of the
word “not”:
a. Today is Thursday.
b. 2 + 1 = 3
c. There is no wind in Illinois.
2. Let p, q, and r, be the propositions:
p: You get an A on the final exam.
q: You do every exercise in this book.
r: You get an A in this class.
Write these propositions using p, q, and r, and logical connectives.
a.
b.
c.
d.
You get an A in this class, but you do not do every exercise in this book.
You get an A on the final, you do every exercise in this book, and you get an A in this class.
To get an A in this class, it is necessary for you to get an A on the final.
You get an A on the final, but you don’t do every exercise in this book; nevertheless, you get
an A in this class.
e. Getting an A on the final and doing every exercise in this book is sufficient for getting an A
in this class.
3. Without using truth tables, show that ~p → (q → r) and q → (p ∨ r) are logically
equivalent.
4. Let D(x), P(x), R(x), and W(x) be the statements
“x is a duck,”
“x is one of my poultry,”
“x is an officer,” and
“x is willing to waltz,”
Express each of these statements using quantifiers, logical connectives, and D(x), P(x),
R(x) and W(x).
No ducks are willing to waltz.
No officers ever decline to waltz.
All my poultry are ducks.
My poultry are not officers.
Some officers are willing to waltz.