Introductory Logic Test #3 November 14, 2005 R. Hammack Name: ________________________ Score: _________

1. Use only the 18 rules of implication or replacement to derive the conclusions of the following arguments.

 (a) 1.   A ⊃ B 2.   B ⊃ D 3.    ~D 4.    A ∨ E /    E

 (b) 1.   (G ∨ X) ⊃ (P∨ S) 2.   ~P ⊃ G 3.   ~P /    S • G

 (c) 1.   (~M ∨ S) ⊃ P 2.    M ⊃ R 3.    R ⊃ S /   P

 (d) 1.   ~(~A ∨ B) 2.   X ⊃ B /    ~X • A

 (e) If grade-school children are assigned daily homework, then their achievement level will increase dramatically. But if grade-school children are assigned daily homework, then their love for learning may be dampened. Therefore, if grade-school children are assigned daily homework, then their achievement level will increase dramatically, but their love for learning may be dampened. (G, A, L)

2. Use conditional proof or indirect proof (and the 18 rules of inference) to establish the truth of the following tautology:  ~M∨ (L ⊃ M)

3. Use the technique of conditional proof to deduce the conclusion of the following argument. (Alternatively, use only the 18 rules.)

 1.  ( M • ~S) ⊃ L 2.   S ⊃ K /    M ⊃ (~K ⊃ L)

4.  Use the technique of indirect proof to deduce the conclusion of the following argument. (Alternatively, use only the 18 rules.)

 1.   N ⊃ O 2.   (N • O) ⊃ P 3.   ~(N ∨ P ) /    ~N

5. Use the method of conditional proof or indirect proof (or both) to deduce the conclusions of the following arguments.

 (a) 1.   C ⊃ (A • D) 2.   B ⊃ (A • E) /   (C ∨ B) ⊃ A

 (b) If government deficits continue at their present rate and recession sets in, then interest on the national debt will become unbearable and the government will default on its loans. If a recession sets in, then the government will not default on its loans. Therefore, government deficits will not continue at their present rate, or a recession will not set in. (C, R, I, D)