Materials

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?