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Written by Dr. Elihu Carranza
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Tuesday, 19 August 2008 20:33 |
Exercise 5.1 | Part A | Part B | | 1 | B | 1 | G | | 2 | E | 2 | A | | 3 | A | 3 | B | | 4 | C | 4 | C | | 5 | F | 5 | D | | 6 | D | 6 | D | | 7 | G | 7 | C | | | | 8 | E | | | | 9 | F | | | | 10 | F | Exercise 5.2 Hawk Newton is good in either science or theology, but not both. Moreover, either he is good at logic or bad at theology. If he is not good in science, he is bad at theology. If he is bad at theology, he is good at logic. What do these four premises imply, if anything? Is Hawk good in anything? In or at what? | 1 | . Hawk is good in either science or theology, but not both. | (s + t)(st)' | | 2 | Hawk is good at logic or bad at theology. | (l + t' ) | | 3 | If he is not good in science, he is bad at theology. | (s' < t' ) | | 4 | If he is bad at theology, he is good at logic. | (t' < l) | | | | | | | | | | | | | | | 1st | 2nd | 3rd | 4th | | | s | l | t | (s + t) | (st)' | (l + t') | (s' < t' ) | (t' < l) | | 1 | T | T | T | T | F | T | T | T | | 2 | T | T | F | T | T | T | T | T | | 3 | T | F | T | T | F | F | T | T | | 4 | T | F | F | T | T | T | T | F | | 5 | F | T | T | T | T | T | F | T | | 6 | F | T | F | F | T | T | T | T | | 7 | F | F | T | T | T | F | F | T | | 8 | F | F | F | F | T | T | T | F | | | i | ii | iii | iv | v | vi | vii | viii | Row #2 is the only row that has true values in columns iv through viii. Notice the values of the propositional variables in that same row. There, Hawk is good at science and logic, but it is false that he is good at theology, at least according to this truth table analysis. One more deduction is possible from the third and fourth propositions: (s' < t' ) and (t' < l) imply (s' < l) by transitive syllogism. If Hawk is not good at science, then he is good at logic.
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