Problem_Set_3_solutions

Problem_Set_3_solutions - V83.0070 Logic Spring 2008 Matt...

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V83.0070 Logic Spring 2008 Matt Kotzen Problem Set 3 Solutions 3.2E: 1b) J |K |J (K J) T |T |T T T T T T |F |T T F T T F |T |F T T F F F |F |F T F T F So the sentence is truth-functionally true 1f) C |D |E |([(C D) & (D E)] & C) & ~E T |T |T | T T T T T T T T T F FT T |T |F | T T T F T F F F T F TF T |F |T | T F F F F T T F T F FT T |F |F | T F F F F T F F T F TF F |T |T | F T T T T T T F F F FT F |T |F | F T T F T F F F F F TF F |F |T | F T F T F T T F F F FT F |F |F | F T F T F T F F F F TF
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So the sentence is truth-functionally false 2b) F |H |(F H) ( F H) T |T | T T T T F FT T T T |F | T T F T F FT T F F |T | F T T T F TF T T F |F | F F F T T TF F F So the sentence is truth-functionally true 2d) A |B |(A B) A T |T | T |F | T F F F T F |T | F |F | So the sentence is not truth-functionally true 4b) True. If one disjunct is always true, then the whole disjunction will always be true too, since a disjunction is true whenever at least one of its disjuncts is true. 4d) True. If one conjunct is always false, then the whole conjunction will always be false too, since a conjunction is false whenever at least one of its conjuncts is false. 4f)
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Problem_Set_3_solutions - V83.0070 Logic Spring 2008 Matt...

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