Problem_Set_2_solutions

# Problem_Set_2_solutions - V83.0070 Logic Spring 2008 Matt...

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V83.0070 Logic Spring 2008 Matt Kotzen Problem Set 2 Solutions 2.1E: 1b) B&C 1d) A&C 1f) B& A 1h) ( A& B)& C 1j) C&(B A) 1l) ((A B) C) 1n) ((A C) B) 2b) Either Albert jogs regularly or he doesn’t. 2d) Neither Albert nor Carol jogs regularly. 2f) It’s not the case that Bob doesn’t jog regularly. 2h) Either Albert or Carol jogs regularly, but it’s not the case that they both do. 2j) At least one of Albert, Bob, and Carol doesn’t jog regularly. 5b) L B 5d) M C 5f) C ( L B) 5h) (C B) A 5j) ( C & B) ⊃∼ A 5l) H (A B) 5n) (H & A) & (B C) 5p) A (B C) 5r) (A H) (L ⊃∼ B) 5t) H ⊃∼ (B&A) 6b) If Carol is a marathon runner, then she jogs regularly. 6d) Carol jogs regularly, but Bob doesn’t. 6f) If any of Alice, Bob, and Carol jog regularly, then they all do. 2.2E: 1b) (F ⊃∼ (G D)) & ( (G ⊃∼ (F D)) & (D ⊃∼ (F G)) ) 1d) (F&(G&D)) 1f) ((F&G) ⊃∼ D) & ( ((F&D) ⊃∼ G) & ((G&D) ⊃∼ F) ) or (F&(G&D)) 1h) ((F&G)&D) 3b) (F ⊃∼ P) & (P ⊃∼ F) 3d) ( R & S) ((F D)

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