Truth-Tables

# Truth-Tables - Todays Topics (10/26) I. II. III. IV. V. VI....

This preview shows pages 1–8. Sign up to view the full content.

3/4/11 Today’s Topics (10/26) I. Truth-Values II. Truth-Functional Connectives III. The Truth-Table for Conjunctions IV. The Truth-Table for Negations V. The Truth-Table for Disjunctions VI. The Truth-Table for Conditionals VII. The Truth-Table for Bi-Conditionals

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3/4/11 I. Truth Values A proposition has the truth-value T just in case it is true. A proposition has the truth-value F just in case it is false. Examples: “Obama is the president” has the truth- value T.
3/4/11 II. Truth-Functional Connectives In propositional logic, we must assume that each of the five propositional connectives are truth- functional connectives . Joe Biden has read Moby Dick. It is not the case that Joe Biden has read Moby Dick. T F F T Joe Biden has read Moby Dick. Sarah believes that Joe Biden has read Moby Dick. T ?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3/4/11 III. Truth-Tables When, or under what conditions, are conjunctions true? When, or under what conditions, are disjunction true? When, or under what conditions, are negations true? When, or under what conditions, are conditionals true?
3/4/11 IV. The Truth-Table for Conjunctions This table tells us that Ø when ‘p’ is true and ‘q’ is true, ‘p & q’ is true; Ø when ‘p’ is true and ‘q’ is false, ‘p &q’ is false; Ø when ‘p’ is false and q is true, ‘p & q’ is p q T T T T F F F T F F F F

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3/4/11 Constructing the Truth-Table for Conjunctions-Step 1 p q We use truth-tables for propositional forms to show when instances of these propositional forms are true or false. To the right of the vertical line, we write the propositional form in question. To the left of the vertical line, we write all of the variables that occur in the propositional form in question. In this case, there are only two —p and q.
3/4/11 Constructing the Truth-Table for Conjunctions-Step 2 p q T T T F F T F F We then list all of the truth-value combinations that p and q can possibly have. Each combination is called a ‘truth-value assignment.’ In propositional logic, we assume that all propositions are either

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 03/03/2011 for the course PHIL 100 taught by Professor Forte during the Spring '08 term at Bridgewater State University.

### Page1 / 26

Truth-Tables - Todays Topics (10/26) I. II. III. IV. V. VI....

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online