KBTU-AbstrMathFall-Lect02

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

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
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
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
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
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 6
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
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 8
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
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Basic Logical Connectives Problems
Image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern