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Lecture03 - PHIL V3411 PHIL G4415 Introduction to Symbolic...

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PHIL V3411 / PHIL G4415 • Introduction to Symbolic Logic Lecture 3 Sentential Logic: The Conjunction Connective
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INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 3 P. 1 The Conjunction Connective (Section 2.1.2) For every pair of sentences A and B there is another sentence called the conjunction of A and B . English: A and B left conjunct right conjunct Symbolization: A B Semantics: A B is T if both A and B are T ; otherwise A B is F Truth table : A B A B T T T T F F F T F F F F Note: the order of the conjuncts makes no difference to the truth- value of the conjunction: Principle of Commutativity : A B has the same truth-value as B A (though they are different sentential expressions)
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INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 3 P. 2 Repeated Applications and Grouping Since the conjunction of two sentences is itself a sentence, it can be conjoined with any other sentence. — The conjunction of A B and C : ( A B ) C — The conjunction of A and B C : A ( B C ) Parentheses are used to distinguish the two sentences. Principle of Associativity : ( A B ) C has the same truth-value as A ( B C ) Conjunction can also be combined with negation: — The conjunction of A
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