KBTU-AbstrMathFall-Lect02

# KBTU-AbstrMathFall-Lect02 - Basic Logical Connectives...

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Basic Logical Connectives Problems Abstract Mathematics MT2116 Lecture 02: Mathematical Logic Sergey Khrushchev International School of Economics Kazakh-British Technical University, Almaty 25.08.2015 / KBTU Sergey Khrushchev

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Basic Logical Connectives Problems Outline 1 Basic Logical Connectives ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements 2 Problems Problems from Books Former Exams Problems Sergey Khrushchev
Basic Logical Connectives Problems ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements Textbook Reading: Biggs N.L. Discrete Mathematics, 2nd ed (Oxford 2002, ISBN 978 0 19 850717 8, 425 pp) Biggs on Google CH 3, 17-24pp Lay S.R. Analysis with an Introduction to Proof, 5th ed (Pearson 2014, ISBN 9781292040240, 365pp) CH 1, 19-40 pp Sergey Khrushchev

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Basic Logical Connectives Problems ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements Logical Connectives: The Connective ‘OR’ There are several simple operations in Logic which allow one to construct more complicated statements from simple ones. We begin with or . Definition Given two statements P and Q the statement P Q is the statement which is true only if one of the statements P or Q is true. Example The statement a = 0 b = 0 is true if a = 0 and is also true if b = 0 regardless of the value of a . This is called the inclusive use of or which is an equivalent notation for . Sergey Khrushchev
Basic Logical Connectives Problems ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements The Truth table of Formal Logical Statements are controlled by Truth Tables. Here is the Truth Table for : P Q P Q T T T T F T F T T F F F Sergey Khrushchev

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Basic Logical Connectives Problems ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements Logical Connectives: The Connective ‘AND’ We consider now and . Definition Given two statements P and Q the statement P Q is the statement which is true only if the both statements P and Q are true. Example The statement a = 0 b = 0 is true if a = 0 as well as b = 0. Sergey Khrushchev
Basic Logical Connectives Problems ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements The Truth table of P Q P Q T T T T F F F T F F F F Sergey Khrushchev

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Basic Logical Connectives Problems ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements The Truth table of ¬ P ¬ P T F F T Sergey Khrushchev
Basic Logical Connectives Problems ‘negation’, ‘or’, ‘and’,and their Truth Tables Logical Equivalence Converse and Contrapositive Statements The Truth Table of Implication: P Q P Q T T T T F F F T T F F T Sergey Khrushchev

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Basic Logical Connectives Problems
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