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1 / The Foundations: Logic and Proofs
TABLE 9 Table for the Bit Operators OR,
AND, and XOR.
x
y
xy
xy
xy
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
Information is often represented
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1.3 Propositional Equivalences
c) Mei walks or takes the bus to class.
d) Ibrahim is smart and hard working.
8. Use De Morgans laws to find the negation of each of t
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1.1 Propositional Logic
5. What is the negation of each of these propositions?
a) Steve has more than 100 GB free disk space on his
laptop.
b) Zach blocks e-mails an
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40. Explain, without using a truth table, why (p q)
(q r) (r p) is true when p, q, and r have the
same truth value and it i
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15.
16.
17.
18.
19.
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a) You get an A in this class, but you do not do every
exercise in this book.
b) You get an A on the fin
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1.2 Applications of Propositional Logic
10. Are these system specifications consistent? Whenever
the system software is being upgraded, users cannot access the file
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1.2 Applications of Propositional Logic
17
often ambiguous. Translating sentences into compound statements (and other types of logical
expressions, which we will introduce later in
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Solving Satisfiability Problems
A truth table can be used to determine whether a compound proposition is satisfiable, or equ
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1 / The Foundations: Logic and Proofs
p r
p
r
p
r
(p r) (p (q r)
p
q
r
r
q r
p (q r)
FIGURE 3 The circuit for (p r) (p (q r).
Exercises
In Exercises 16, translate
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44. Show that and form a functionally complete collection of logical operators. [Hint: First use a De Morgan law to show th
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33.
34.
35.
36.
37.
38.
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1 / The Foundations: Logic and Proofs
saw both Smith and Jones with Cooper the day of the
killing and that either Smith or Jones must hav
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1.1 Propositional Logic
24. Write each of these statements in the form if p, then q
in English. [Hint: Refer to the list of common ways to express conditional statem