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1-24-07, Lecture 03

# 1-24-07, Lecture 03 - PHIL V3411 PHIL G4415 Introduction to...

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PHIL V3411 / PHIL G4415 • Introduction to Symbolic Logic Lecture 3 Sentential Logic: The Conjunction Connective

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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)
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 and ¬ B A " ¬ B — The conjunction of ¬ A and B ¬ A " B

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1-24-07, Lecture 03 - PHIL V3411 PHIL G4415 Introduction to...

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