Logic

11
Logic The Lost Art of Argument

description

Logic. The Lost Art of Argument. Logic - Review. Proposition – A statement that is either true or false (but not both) Conjunction – And Disjunction – Or Negation – Not Truth Tables can be used to determine Equivalence Equivalence – Two propositions have the same truth values. - PowerPoint PPT Presentation

Transcript of Logic

Page 1: Logic

Logic

The Lost Art of Argument

Page 2: Logic

Logic - Review

Proposition – A statement that is either true or false (but not both)

Conjunction – And

Disjunction – Or

Negation – Not

Truth Tables can be used to determine Equivalence

Equivalence – Two propositions have the same truth values

Page 3: Logic

Conditional Sentences

Definition: Conditional Sentence – Given two propositions P, Q.P QP implies QIf P, then Q

Examples:If it is raining, then the roof is wet.If I am late for class, then it is Monday.If you don’t wear your lucky shirt, then you will lose the game.If 4 is an even number, then 4 > 8If the moon is round, then the chair is blue

Page 4: Logic

Conditional Sentences

Definition: Antecedent – If P Q, then P is called the antecedent.

Definition: Consequent – If P Q, then Q is called the consequent.

Identify the Antecedent and Consequent in the following:

If it is raining, then the roof is wet.

If I am late for class, then it is Monday.

Page 5: Logic

Conditional Sentences

Definition: Negation – For propositions P and Q, the negation of P Q is ~P ~Q

Examples:

If it is raining, then the roof is wet.

Negation: If it is not raining, then the roof is not wet.

If I am late for class, then it is Monday.

Negation: If I am not late for class, then it is not Monday.

Page 6: Logic

Conditional Sentences

Definition: Converse – For propositions P and Q, the converse of P Q is Q P

Examples:

If it is raining, then the roof is wet.

Converse: If the roof is wet, then it is raining.

If I am late for class, then it is Monday.

Converse: If it is Monday, then I am late for class.

Page 7: Logic

Conditional Sentences

Definition: Contrapositive – For propositions P and Q, the contrapositive of P Q is (~Q) (~P)

Examples:

If it is raining, then the roof is wet.

Contrapositive: If the roof is not wet, then it is not raining.

If I am late for class, then it is Monday.

Contrapositive: If it is not Monday, then I am not late for class.

Page 8: Logic

Conditional Sentences

Transitive Property of Conditional Sentences: P Q, Q R, then P R

Examples:

If it is raining, then I am late for class.

If I am late for class, then it is Monday.

If it is raining, then it is Monday.

Page 9: Logic
Page 10: Logic

Logic - Review

Definition: Conditional Sentence – Given two propositions P, Q.P QP implies QIf P, then Q

Definition: Antecedent – If P Q, then P is called the antecedent.Definition: Consequent – If P Q, then Q is called the consequent.

Definition: Negation – For propositions P and Q, the negation of P Q is ~P ~Q

Definition: Converse – For propositions P and Q, the converse of P Q is Q P

Definition: Contrapositive – For propositions P and Q, the contrapositive of P Q is (~Q) (~P)

Page 11: Logic

Logic – Next Time

Syllogisms

All the old articles in this cupboard are cracked

All jugs in this cupboard are old

Nothing in this cupboard that is cracked will hold water


Propositional Logic and Pridicate logic

Propositional Logic and Pridicate logic

CT455: Computer Organization Logic gate. Lecture 4: Logic Gates and Circuits Logic Gates Logic Gates Logic Gates Logic Gates The Inverter The Inverter.

CT455: Computer Organization Logic gate. Lecture 4: Logic Gates and Circuits Logic Gates Logic Gates Logic Gates Logic Gates The Inverter The Inverter.

Techniques for Solving Logic Puzzles. Logic Puzzles Logic puzzles operate using deductive logic. Logic puzzles operate using deductive logic. A well-designed.

Techniques for Solving Logic Puzzles. Logic Puzzles Logic puzzles operate using deductive logic. Logic puzzles operate using deductive logic. A well-designed.

Modal Logic, Temporal Logic and the Logic of Agency

Modal Logic, Temporal Logic and the Logic of Agency

Gates and Logic: From Transistors to Logic Gates and Logic ......Gates and Logic: From Transistors to Logic Gates and Logic Circuits [Weatherspoon, Bala, Bracy, and Sirer] Prof. Hakim

Gates and Logic: From Transistors to Logic Gates and Logic ......Gates and Logic: From Transistors to Logic Gates and Logic Circuits [Weatherspoon, Bala, Bracy, and Sirer] Prof. Hakim

Logic Design Sequential Logic (Chapter 3)bhagiweb/cs2461/lectures/logic4.pdf · Logic Design Sequential Logic (Chapter 3) So Far: Combinational Logic Combinational Logic: • Always

Logic Design Sequential Logic (Chapter 3)bhagiweb/cs2461/lectures/logic4.pdf · Logic Design Sequential Logic (Chapter 3) So Far: Combinational Logic Combinational Logic: • Always

Gates and Logic: From Transistors to Logic Gates and Logic ... · Goals for Today 2 • From Switches to Logic Gates to Logic Circuits • Logic Gates • From switches • Truth

Gates and Logic: From Transistors to Logic Gates and Logic ... · Goals for Today 2 • From Switches to Logic Gates to Logic Circuits • Logic Gates • From switches • Truth

Prop Logic 1-Logic

Prop Logic 1-Logic

Introduction to Logic Relational Logic

Introduction to Logic Relational Logic

KemPtah Logic (Black Supremem Logic)

KemPtah Logic (Black Supremem Logic)

Combining Description Logic, Autoepistemic Logic and Logic Programming

Combining Description Logic, Autoepistemic Logic and Logic Programming

AN INTRODUCTION TO LOGIC - The Best Schools to Logic 1 AN INTRODUCTION TO LOGIC By: ... Mathematical Logic, ... Introduction to Logic 3 GENERAL INTRODUCTION

AN INTRODUCTION TO LOGIC - The Best Schools to Logic 1 AN INTRODUCTION TO LOGIC By: ... Mathematical Logic, ... Introduction to Logic 3 GENERAL INTRODUCTION

Today’s Topics Digital Logic Design Digital Logic Design Boolean Logic Boolean Logic Digital Logic Circuits Digital Logic Circuits.

Today’s Topics Digital Logic Design Digital Logic Design Boolean Logic Boolean Logic Digital Logic Circuits Digital Logic Circuits.

Predicate Logic. From Propositional Logic to Predicate Logic Last week, we dealt with propositional (or truth-functional) logic: the logic of truth- functional.

Predicate Logic. From Propositional Logic to Predicate Logic Last week, we dealt with propositional (or truth-functional) logic: the logic of truth- functional.

3 Logic gates and logic circuits...3 Logic gates and logic circuits. 3 Logic gates and logic circuits. In this chapter you will learn about: • logic gates • truth tables • logic

3 Logic gates and logic circuits...3 Logic gates and logic circuits. 3 Logic gates and logic circuits. In this chapter you will learn about: • logic gates • truth tables • logic

Propositional Logic, Predicate Logic, and Logic Programmingcs500.cs.ua.edu/logic.pdfPropositional Logic, Predicate Logic, and Logic Programming. 2 ... For logical propositions to have

Propositional Logic, Predicate Logic, and Logic Programmingcs500.cs.ua.edu/logic.pdfPropositional Logic, Predicate Logic, and Logic Programming. 2 ... For logical propositions to have

Modern Logic - Introduction to Logic

Modern Logic - Introduction to Logic

The Logic of PartitionsWhy Partition Logic took so long to develop Boolean logic mis-specified as logic of "propositions." Boolean logic correctly specified as logic of subsets.

The Logic of PartitionsWhy Partition Logic took so long to develop Boolean logic mis-specified as logic of "propositions." Boolean logic correctly specified as logic of subsets.

Modal Logic, Epistemic Logic

Modal Logic, Epistemic Logic

AB-Fuzzy Logic -Logic Operations

AB-Fuzzy Logic -Logic Operations