School

University of WaterlooDepartment

Electrical and Computer EngineeringCourse Code

ECE103Professor

Martin PeiStudy Guide

FinalThis

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ECE 103

FINAL EXAM

STUDY GUIDE

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The$statement$P"AND"Q is$called$the$conjunction of$P"and"Q and$is$true$

when$ both$

P$and$Q$are$true$and$false$otherwise.$

1.

The$statement P"OR"Q is$called$the$disjunction of$P"and"Q and$is$true$

when$ at$least$

one$of$P$and$Q$is$true$and$false$otherwise.$

2.

The$statement$NOT"P is$called$the$negation of$Pand$is$true$when$P$is$

false$and$

false$when$P$is$true.$

3.

Definition$1.2.1$Let$P$and$Q$be$two$statements.$

Implications:$“If"P,"then"Q” where$statement$ P$is$called$the$hypothesis$ and$

statement$Q$is$called$the$conclusion.$(“P$⇒Q”)

Truth$Table$

P$

Q$

P⇒Q$

(NOT$P)$OR$Q$

T$

T

F

F$

T$

F$

T$

F$

T$

F$

T$

T$

T$

F$(vacuous$ statement)

T

T$

Biconditional$Statement:$P"

⇔

Qis$true$precisely$when$P$and$Q$have$the$same$

truth$value.$It$is$read,$“P$if$and$only$if$Q.”$

The$truth$table$is$readily$found.$

P$

Q$

P⇔Q$

T$

T

F

F$

T$

F

T$

F$

T

F

F

T$

Statements

Wednesday,$ June$17,$2015

12:06$AM

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⇔

Tautology:$A$statement$that$is$always$true

$$$$$$$P$⇒(Q$AND$R)$$⇔(P$⇒Q)$AND$(P$⇒R)$

Example: P$⇒(Q$OR$R)$⇔(P$AND$(NOT$Q))$⇒R$

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