082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

5 Discretemathematics
Contents 5.1 Introduction 175
5.2 Settheory 175
5.3 Logic 183
5.4 Booleanalgebra 185
Reviewexercises5 197
5.1 INTRODUCTION
The term discrete is used to describe a growing number of modern branches of mathematics
involving topics such as set theory, logic, Boolean algebra, difference equations
and z transforms. These topics are particularly relevant to the needs of electrical and
electronic engineers. Set theory provides us with a language for precisely specifying a
great deal of mathematical work. In recent years this language has become particularly
important as more and more emphasis has been placed upon verification of software.
Boolean algebra finds its main use in the design of digital electronic circuits. Given
thataverylargeproportionofelectroniccircuitsaredigitalratherthananalogue,thisis
animportantareaofstudy.Digitalelectroniccircuitsconfinethemselvestotwoeffective
voltagelevelsratherthantherangeofvoltagelevelsusedbyanalogueelectroniccircuits.
Thesemakethemeasiertodesignandmanufactureastolerancesarenotsocritical.Digital
circuits are becoming more complex each year and one of the few ways of dealing
withthiscomplexityistousemathematics.Oneofthelikelytrendsforthefutureisthat
moreandmorecircuitdesignswillbeprovedtobecorrectusingmathematicsbeforethey
areimplemented.Differenceequationsandztransformsareofincreasingimportance
in fields such as digital control and digital signal processing. We shall deal with these
inChapter 22.
5.2 SETTHEORY
Asetisany collection of objects,things or states.