MA112-Lecture_Notes-OH-L04

MA112-Lecture_Notes-OH-L04 - MA112 Discrete Mathematics...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 1 MA112 Discrete Mathematics Omar Hamdy [email protected] Lecture Notes 4
Background image of page 1

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

View Full DocumentRight Arrow Icon
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 2 Review: Predicate Logic • Propositions do not have centric meanings. They cannot generalize facts. • Predicate Logic explicitly models objects and their attributes. • Allows to build statements with variables. • Allows to build statements for group of objects. • When applying a predicate to a variable subject denoted by P(x), we obtain a propositional function.
Background image of page 2
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 3 Review: Quantifiers • Predicate logic gives the ability to make a statement about groups of subjects. • These are called quantified statements • There are two types of quantifiers: – Universal: , reads for all • All engineers have engineering degree – Existential: , reads there exists • Some engineers have double majors
Background image of page 3

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

View Full DocumentRight Arrow Icon
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 4 Review: Quantifiers Def: The universal quantification of P(x) is the proposition “P(x) is true for all values of x in the universe of discourse”. Def: The existential quantification of P(x) is the proposition “There exists and element in the universe of discourse such that P(x) is true”.
Background image of page 4
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 5 Quantification Summary • Quantification converts a propositional function into a proposition by substituting variables with values from the universe of discourse. P(x) is false for all x. There is some x for which P(x) is true x P(x) There is an x where P(x) is false P(x) true for all x x P(x) When False? When True? Statement
Background image of page 5

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

View Full DocumentRight Arrow Icon
MA112 Discrete Mathematics Dr. Omar Hamdy Summer 2010 6 Nested Quantifiers • Nested quantifiers is sometimes necessary to capture the relations and meanings of predicate logic statements. There is an animal which is faster than all
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/06/2011 for the course MA 112 taught by Professor Omarhamdy during the Spring '10 term at Helwan University, Helwan.

Page1 / 25

MA112-Lecture_Notes-OH-L04 - MA112 Discrete Mathematics...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online