MIT24_241F09_handout04 - ( B C ) Argument ( ): B C B A P 1...

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Logic I Fall 2009 Session 4 Handout Using shortened truth-tables (STTs) to determine the TV of a compound given TVs for the atomic components. A B C (A B) (C A) F T T Building STTs in reverse to determine whether a compound sentence can possibly have a certain TV. J K K ∨∼ J) P is truth-functionally true . . . Can be proven by. . . Can be refuted by. . . P is truth-functionally false . . . Can by proven by. . . Can be refuted by. . . Notions and notation to know Curly braces for sets: { A, B, { C } , { C, D } , . . . } Set union. { A, B, C } ∪{ B, C, D } = Variables for sets of sentences:Γ n The empty set: or {} . Unit / singleton set Γ is truth-functionally consistent . . . Can be established by. . . Inconsistency of Γ can be established by. . . A set Γ of SL sentences truth-functionally entails a sentence P no TVA makes every member of Γ true but P is false. In other words, P is true on every TVA that makes all members of Γtrue. Notation:Γ 1 ± P. Also, note: ± Γabbreviates ± Γ.
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An argument in SL is a set of SL sentences with one designated as the conclusion and the rest designated as premises. E.g.: A
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Unformatted text preview: ( B C ) Argument ( ): B C B A P 1 . . . P n is truth-functionally valid iF no TVA makes P 1 , . . . P n true and C false. C We can connect truth-functional entailment with truth-functional validity: In the denition of truth-functional entailment, let be { P 1 , . . . P n } , and let P be C. P 1 . . Thus, P . n is valid iF { P 1 , . . . P n } truth-functionally entails C. C Prove that Argument ( ) is valid and that its premises truth-functionally entail its conclusion by means of a truth-table. A B C MIT OpenCourseWare http://ocw.mit.edu 24.241 Logic I Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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This note was uploaded on 01/25/2012 for the course PHIL 201H1F taught by Professor Derekallen during the Fall '10 term at University of Toronto- Toronto.

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MIT24_241F09_handout04 - ( B C ) Argument ( ): B C B A P 1...

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