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Written by Dr. Elihu Carranza
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Tuesday, 19 August 2008 20:24 |
Exercise 5.1: Truth Table - Functions
Part A Instructions: Match the truth table values in the columns, a through g, with the correct forms, 1 through 7. | | | a | b | c | d | e | f | g | | x | y | | | | | | | | | T | T | T | T | F | F | T | F | F | | T | F | F | F | T | T | T | F | F | | F | T | T | F | T | F | T | F | T | | F | F | T | F | T | F | F | T | T | | 1 | conjunction | _________ | | 2 | disjunction | _________ | | 3 | implication | _________ | | 4 | contradiction of conjunction | _________ | | 5 | contradiction of disjunction | _________ | | 6 | contradiction of implication | _________ | | 7 | contradiction of x | _________ | Part B Instructions: Match the truth table values in the columns, a through g, with the correct forms, 1 through 10. | | | a | b | c | d | e | f | g | | p | q | | | | | | | | | T | T | T | F | F | T | T | T | F | | T | F | T | F | T | F | F | T | F | | F | T | T | F | T | T | F | F | F | | F | F | T | F | T | T | F | F | T | | ___ 1. (p + q)' | ___ 6. (pq')' | | ___ 2. (pp')' | ___ 7. (p' + q') | | ___ 3. (p + p')' | ___ 8. (p' + q')' | | ___ 4. (pq)' | ____9. (p < p')' | | ___ 5. (p' + q) | ___ 10. (p' + p')' | Exercise 5.2: Truth Table Analysis
Instructions: Do a truth table analysis of the following propositions. 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 | | | | | | | 2 | T | T | F | | | | | | | 3 | T | F | T | | | | | | | 4 | T | F | F | | | | | | | 5 | F | T | T | | | | | | | 6 | F | T | F | | | | | | | 7 | F | F | T | | | | | | | 8 | F | F | F | | | | | | | | i | ii | iii | iv | v | vi | vii | viii |
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