Section 1.1

Materials

• Handout
• Lecture Slides

Introduction

Remember that discrete is the study of decision making in non-continuous systems. That is, it is mathematics when there are a finite number of numbers.

We begin this course by studying Logic. More specifically, we are going to study Propositional Logic which is a number system that works in binary. That is, two numbers - one and zero - which equate to true and false respectively.

Vocabulary

• logic
• proposition
• truth value
• compound proposition
• logical operation
• conjunction
• truth table
• disjunction
• exclusive or
• inclusive or
• negation

p	q	p q	p q	p q	p	q
T	T	(1)	(5)	(9)	(13)	(17)
T	F	(2)	(6)	(10)	(14)	(18)
F	T	(3)	(7)	(11)	(15)	(19)
F	F	(4)	(8)	(12)	(16)	(20)

We normally think of the symbol T to be equivalent to the number 1 and the symbol F to be equivelant to the number 0.

Given this fact, what mathematical expression is equivalent to conjunction? What mathematical fact is (sort of) equivalent to disjunction?