Jeff Wickstrom
Jason Slattery
Discrete Mathematics - Logic
Lesson Plans
Discrete Mathematics
Discrete mathematics, also called finite mathematics, is the study of mathematical
structures that are fundamentally discrete, in the sense of not supporting or requiring the
notion of continuity. Most, if not all, of the objects studied in finite mathematics are
countable sets, such as integers, finite graphs, and formal languages.
Discrete mathematics has become popular in recent decades because of its applications to
computer science. Concepts and notations from discrete mathematics are useful to study or
describe objects or problems in computer algorithms and programming languages. In some
mathematics curricula, finite mathematics courses cover discrete mathematical concepts for
business, while discrete mathematics courses emphasize concepts for computer science
majors.
Text: Mathematical Ideas, Miller, Heeren, Hornsby, Pearson Addison-Wesley, 10th edition
Internet Links for information on selected topics:
www.mysterymaster.com/puzzles.html
www.conceptispuzzles.com/
www.edhelper.com/logic_puzzles.htm
www.thakur.demon.nl/
http://crpuzzles.com/logic/index.html
www.puzzlersparadise.com/page1034.html
http://en.wikipedia.org/wiki/Discrete_mathematics
http://archives.math.utk.edu/topics/discreteMath.html
http://mathforum.org/discrete/discrete.html
Day One and Two
Pre-Test (True/False test)
Discrete Mathematics- Logic
Pre-Test
Name
Circle your response to the following True/False questions.
True/False
1.
2 is an ugly number is a statement.
True/False
2. The negation of a statement is always False.
True/False
3. Given the statement “p” is True, the compound statement p q will
result in a True statement.
True/False
4. Given the statement “p” is False, the compound statement p q will
result in a False statement.
True/False
5. The truth table for the compound statement ( p q ) r will have 8
rows.
True/False
6. There exists a whole number that is not a natural number.
True/False
7. There exists an irrational number that is not real.
True/False
8. A conjunction is formed by using the connective “and”.
True/False
9. 3 + 1 = 5 or 5 - 2 = 3 is a true statement.
True/False
10. A disjunction is not formed by using the connective “or”.
True/False
11. Conditionals contain two statements the antecedant and the
consequent.
True/False
12. If the antecedent is false, then p q is automatically true.
True/False
13. If the consequent is false, then p q is automatically true.
True/False
14. The negation of p q is p ~ q .
True/False
15. From De Morgan’s Laws ~ ( p q ) ~ p ~ q
Reading assignment: pp. 94 – 99
Topics:
1. Statements
a. Definition of a statement
b. Compound statements
c. Logical connectives
d. Negations
2. Quantifiers
a. Universal
1. all, each, every, and no(ne)
b. Existential quantifiers
1. some, there exists, and (for) at least one
c. Negations of Quantified Statements
3. Sets of Numbers
a. Natural
b. Whole numbers
c. Integers
d. Rational Numbers
e. Real Numbers
f. Irrational Numbers
Allotted Time: Two 50-minute classes
Students will be able to understand the definitions of Statements and Quantifiers. Students
will be able to determine what makes a statement a statement. Students will be able to
negate statements by the use of quantifiers. Students will be able to negate mathematical
statements. Students will be able to translate symbolic compound statements into words.
Students will be able to convert compound statements into symbols. Students will be able
to decide whether statements involving quantifiers are true or false. Using Sets of
Numbers, students will be able to determine which sets of numbers are subsets of other sets
of numbers.
Examples:
A statement is defined as a declarative sentence that is either true or false, but not both
simultaneously
Negate the following Existential statement: “Some cats have fleas.” The negation would
be “No cat has fleas.”
Given p represents “It is 80˚ today,” and let q represent “It is Tuesday.” Write the
symbolic statement in words. ~p q becomes “It is not 80˚ today and it is Tuesday”
Day Three and Four
Introductory Activity: Show Life by the Numbers Video #6 , A New Age, Information Age
Reading Assignment: pp. 102-110
Internet Assignment: research Boolean Algebra
Topics:
1. Truth Tables
a. Conjunction
b. Disjunction
c. Negation
2. Mathematics of Truth Tables
a. Rows of a truth table
b. Creating the left hand column of the truth table
3. De Morgan’s Laws
Allotted Time: Two 50-Minute classes
Students will examine Truth Tables and the Boolean Algebra Logic used to create them.
Students with be able to work with the Conjunction, Disjunction and Negation. Students
will be able to set up the left hand column of Truth Tables by using the powers of two
mathematics involved. Students will be able to read completed Truth Tables and determine
a final logical value for inputted information. Students will be able to determine equivalent
statements by using De Morgan’s Laws.
Examples:
Negation
p
~p
T
F
F
T
Conjunction
pq
p q
T T
T
T F
F
F T
F
F F
F
From De Morgan’s Laws
Disjuntion
p
q
T
T
T
F
F
T
F
F
pq
T
T
T
F
~ ( p q ) ~ p ~ q and ~ ( p q ) ~ p ~ q
Day Five and Six
Reading assignment: pp. 113 – 120
Topics:
1. Conditional
a. Antecedent
b. Consequent
c. If/Then logic
d. Special Characteristics of Conditional Statements
e. Tautologies
2. Negation of a Conditional
3. Writing a Conditional as an “or” Statement
4. Circuits
Allotted Time: Two 50-minute classes
Students will be able to rewrite statements using the if … then connective. Students will
be able to decide whether conditional statements are true or false. Students will be able
to express compound symbolized statements in words. Students will be able to use
symbols to rewrite compound statements. Students will be able to construct truth tables
using the Conditional. Students will be able to write negations of Conditional statements.
Students will be able to rewrite Conditional Statements using the connective “or”.
Students will be able to draw circuits representing statements.
Examples:
Conditional
p
q
T
T
T
F
F
T
F
F
pq
T
F
T
T
Rewrite of statement using if…then:
Original Statement: “It is difficult to study when you are distracted”
Rewrite:
“If you are distracted, then it is difficult to study”
Day Seven and Eight
Reading assignment: pp. 133 – 136
Topics:
1. Logic Puzzles
a. Solving logic puzzles using
charts
Allotted time: Two 50-minute classes
Students will be able to solve logic puzzles using
charts.
Sample Problem:
Five Houses
Five houses of different colors are in a row. Each is owned by a man
with a different nationality, hobby, pet and favorite drink.
1.
2.
3.
4.
5.
6.
7.
8.
The Englishman lives in the red house.
The Spaniard owns dogs.
Coffee is drunk in the green house.
The Ukrainian drinks tea.
The green house is directly to the right of the white one.
The stamp collector owns snails.
The antiques collector lives in the yellow house.
The man in the middle house drinks milk.
9. The
10. The
11. The
12. The
13. The
14. The
Norwegian lives in the first house.
man who sings lives next to the man with the fox.
man who gardens drinks juice.
antiques collector lives next to the man with the horse.
Japanese man's hobby is cooking.
Norwegian lives next to the blue house.
Who drinks water and who owns the zebra?
Chart
House
Color
Nationality
Hobby
Pet
1st House
2nd House
3rd House
4th House
5th House
Visit Mystery Master at www.mysterymaster.com
The Master of Logic Puzzles
Day Nine
Assessment: Post-Exam
Drink