The University of Western Ontario London Canada Department of PhilosophyPhilosophy 212 001 UWIntroduction to Logic L FalkensteinMidYear Test Wednesday December 14 20113 hours 700pm EC 2155Closed Book Page one of one page Answer All Questions1 Define the following 5 a Logical inconsistency A set of sentences is logically inconsistent if and only if there is a contradiction in supposing all the sentences in the set are trueAlternative answers iff it it is impossible for all the sentences in the set to be true iff no set of sentences with those forms contains sentences that are all true b Truth functional inconsistency A set of sentences is tf inconsistent if and only if there is no truth value assignment on which all the sentences in the set are true c Modal inconsistencyA set of sentences is minconsistent if and only if there is no world of any model in which all the sentences in the set are true d Converse of a conditional PQThe converse of a conditional PQ is QP e Dual of P and of P v QThe dual of P is PThe dual of P v Q is PQNote that before a dual can be formed by removingthere have to be enough s to removeWhere one or more is missing the dual can only be formed by adding them2Which of the following is the contradictory of PQIs it possible for a sentence to have more than one contradictoryA sentence can have more than one contradictory if it is a negationBoth P and P are contradictories of PSince PQ is not a negation but a conditional it has only one contradictory the sentence that is its negation and no other 2 aPQ bPQ cPQ dPQ e PQ3For each of the following circle T if the sentence is true or F if the sentence is false4 T F a Every argument whose conclusion is logically true is valid T F b Every argument with true premises and a true conclusion is valid T F c Every sound argument has a true conclusion T F d Every pair of true sentences is a pair of logically equivalent sentences

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