Exercises in Logic III PDF

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Exercises in Logic III...

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Exercises in Logic III (Logical Equivalence and Validity of argument) ref.

Discrete mathematics and Its Applications by Kenneth Rosen Discrete Mathematical Structures for Computer Sciences” by Kolman, Bernard, Busby Discrete Structures: an introduction to Mathematics for computer,” science, Norris, Fletcher

I. Prove that the following statements are tautology using common tautologies.] 1. 2. 3. 4. 5. 6.

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7. 8. 9. 10. 11. 12. II Establish the validity of the following arguments using a step-by-step procedure and identifying each rule or common tautology that validate each steps. a)

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c)

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III. Is the argument valid or not? If valid, give the rule of inference that validates it, if invalid; use a truth table or give a counterexample to show the arguments are not a tautology. 1. If the trees are cut, then there will be flooding. The trees are not being cut. Therefore there won’t be flooding. 2

2. If Babyboo swallowed the basketball, then his stomach will be enlarged. Babyboo’s stomack is enlarged. Therefore he swallowed the basketball. 3. For this marriage to succeed, it is enough that Eba isn’t fond of apples. This marriage has succeeded. Therefore Eba isn’t fond of apples.

4. If there is a tikbalang living in the tree, you’ll lose your way home. You’ve been able to get home. Therefore there is no tikbalang in that tree.

5. The house at the corner either has a red roof or a blue roof. If the roof is blue, then the house is Jon’s. If it is Mark’s, then the roof is tiled. Therefore if the house is not Jon’s then it is Mark’s.

6. If Margaret goes out with either Bobo or Dodo, her mother will be angry. If Margaret’s sister accompanies her, she won’t go out with Bobo. Her sister accompanies her and she does not go out with Dodo. Therefore her mother is not angry.

7. It is raining and Annabelle loves me. If it rains, then the roof leaks and Annabelle loves me. If the roof leaks, then Annabelle sings or the toads croak. Annabelle doesn’t sing. Therefore the toads don’t croak.

8. The cat lies under the chair and the frog sits on the lotus pad. If the cat lies under the chair, then the mouse will eat the cracker and the frog will sit on the lotus pad. If the mouse eats the cracker, then the rooster will crow or the carabao will eat hay. The rooster doesn’t crow. Therefore the carabao eats hay.

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