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