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MATH 1P66
MATHEMATICAL REASONING
Instructor: Jeff Haroutunian
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View Full Document A few notes
Course outline
Course materials will be found on Sakai
http://lms.brocku.ca
Course text (not required but recommended) is
“Discrete Mathematics and Its Applications, 6/e”, by
Kenneth Rosen, McGraw Hill, 2007
Purpose of the course
A simple approach
Proposition
A
proposition
is a declarative sentence (i.e. a sentence that
declares a fact) that is either true or false, but not both.
Examples of propositions:
Today is Monday
1+1=3
We do not live in Canada
Not propositions:
1+4
Hahahahaha!
What time is it?
Pay attention.
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View Full Document Truth Value
We talk about “truth values” of propositions in this
course
Examples: The truth value of
“Today is Monday” is True today, but not any other day
of the week.
1+1=3 is False
Note that the truth value needn‟t be known.
Example: “Aliens exist” has an unknown truth value but
it is still a proposition because the truth value is
definitely either True or False but not both.
Propositional Logic
Propositional Logic
(or
Propositional Calculus
) is
the area of logic that deals with propositions
Originally developed by Aristotle over 2300 years
ago
The first set of lectures will deal with propositional
logic
We now turn our attention to
Compound
Propositions
which are formed by combining
existing propositions with logical operators
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View Full Document Conventions
Before we proceed we establish a few conventions:
Propositions are denoted by using
Propositional
Variables
, typically letters
p
,
q
,
r
,
s
,…
Example: We can define a propositional variable
p
as
the proposition “It is sunny today.”
As we previously mentioned a proposition has a truth
value of either True or False, which we will denote as
T
and
F
respectively.
Negation
The
Negation
of a proposition
p
(denoted by
)
is the statement “It is not the case that
p.”
Example:
p
: “It is sunny today.”
“It is not the case that it is sunny today.”
or
more
simply put “It is not sunny today.”
q:
“At least 5cm of snow fell yesterday.”
“It is not the case that …”
or
“More than 5cm of
snow fell yesterday.”
What about “At most 5cm of snow fell yesterday.”
p
:
p
:
q
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This note was uploaded on 06/01/2010 for the course MATH 1P66 taught by Professor Jeffharoutunian during the Spring '10 term at Brock University, Canada.
 Spring '10
 JEFFHAROUTUNIAN
 Math

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