Unit 4 2010 Answers - UNIT 4 SEMANTICS FUN WITH TRUTH-TABLES 4.3 EG1 ~R S R T T F F A contingent sentence S T F T F ~ F F T T R T T F F T F T T S T

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Logic Unit 4: Semantics © Niko Scharer 1 UNIT 4 SEMANTICS: FUN WITH TRUTH-TABLES 4.3 EG1 ~R S R S ~ R S T T F T T T T F F T F F F T T F T T F F T F T F A contingent sentence. ~(R S) R S ~ ( R S ) T T F T T T T F F T T F F T F F T T F F T F F F A contingent sentence. 4.3 EG2 Let’s do a truth-table for the sentence: (Q ~R) ~ (P Q) Since there are 3 atomic sentences, there will be 2 3 possible TVA’s. That’s 8 rows. Truth-table for: ( Q ~ R ) ~ (P Q ) * * P Q R ( Q ~ R) ~ ( P Q ) T T T T T F T F F T T T T T F T T T F F F T T T T F T F F F T F T T F F T F F F T T F T T T F F F T T T T F T F F F T T F T F T T T F F F F T T F F T F F F T F F F T F F F F F T T F F F F T F Not a contradiction. It’s contingent, as we can see from the fourth row.
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Logic Unit 4: Semantics © Niko Scharer 2 4.4 EG1: Let’s try it out. Are the following sentences tautologous, contradictory or contingent? a) ~P Q ( P Q ) : removed parentheses for informal notation TAUTOLOGY * * P Q ( ~ P Q ) (P Q ) T T F T T T T T T T T F F T F F T T F F F T T F T T T F T T F F T F T F T F T F b) ~ ( ~ P ~ Q) (Q ~ P) CONTRADICTION * * P Q ~ ( ~ P ~ Q ) ( Q ~ P ) T T T F T F F T F T F F T T F F F T T T F F F T F T F T F T F T F T F T T T F F F F T F T T F F F T T F c) ~ (P (P Q)) Contingent. P Q ~ ( P ( P Q )) T T F T T T T T T F T T F T F F F T T F F F T T F F T F F F T F 4.4 EG2 a) Are these sentences equivalent? YES. ( P ~Q) ( Q P ) P Q (P ~ Q) (Q P) T T T T F T T T T T F T T T F F T T F T F F F T T F F F F F T T F F T F
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Logic Unit 4: Semantics © Niko Scharer 3 b) Are these sentences consistent? yes ~ ( P Q) ( P Q ) P Q ~ (P Q) (P Q) T T F T T T T T T T F F T T F T F F F T F F T T F F T F F T F F F F T F c) Are these sentences consistent, equivalent or neither? neither. ( ~ P Q) ( Q P ) NEITHER, INCONSISTENT P Q (~ P Q) (Q P) T T F T F T T T T T F F T F F F T T F T T F T T T F F F F T F F F F T F 4.4 EG3: Is this argument valid? (P ~Q) R . ~ R Q. ~P Q Does { ((P ~Q) R ), (~ R Q) } tautologically imply (~P Q)? VALID , TAUTOLOGICAL IMPLICATION P Q R ((P ~ Q) R) (~ R Q) (~ P Q) T T T T F F T T T T F T T T T F T T T Y T T F T F F T F F F T F T T T F T T T T F T T T T F T T F F T F F T F T T F T F F T T T F T F T T F T F T F T T F Y F T T F F F T T T T F T T T T T F T T Y F T F F F F T F F F T F T T T T F T T F F T F F T F T T F F T F F T T F F F F F F F F T F F F F T F T F T T F F F
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Logic Unit 4: Semantics © Niko Scharer 4 4.4 E1: Construct a full truth-table for each of the following sentences. Determine whether each sentence is a tautology, a contradiction or a contingent sentence.
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This note was uploaded on 02/01/2012 for the course PHL PHL245 taught by Professor Scharer during the Winter '11 term at University of Toronto- Toronto.

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Unit 4 2010 Answers - UNIT 4 SEMANTICS FUN WITH TRUTH-TABLES 4.3 EG1 ~R S R T T F F A contingent sentence S T F T F ~ F F T T R T T F F T F T T S T

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