L1[1] - MATH 1P66 MATHEMATICAL REASONING Instructor: Jeff...

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MATH 1P66 MATHEMATICAL REASONING Instructor: Jeff Haroutunian
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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
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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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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.
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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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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.
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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.

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L1[1] - MATH 1P66 MATHEMATICAL REASONING Instructor: Jeff...

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