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Truth-Tables

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

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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

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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. “Sarah Palin is the president” has the
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 ? F ?

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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 p & q T T T T F F F T F F F F

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3/4/11 Constructing the Truth-Table for Conjunctions-Step 1 p q 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. In this case, that is p & q. 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 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 true or false. So, if there are only two variables, the number of possible truth-value combinations will be four. That’s why this table has four rows.

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

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