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Category > Computer Science Posted 19 Sep 2017 My Price 10.00

propositional logic

Using propositional logic, including the rules in Table 1.14, prove that each argument in below Exercises 1-7 is valid. Use the statement letters shown.

1. If the program is efficient, it executes quickly: Either the program is efficient, or it has a bug. However, the program does not execute quickly. Therefore it has a bug.

E, Q, B

2. If Jane is more popular, then she will be elected. If Jane is more popular, then Craig will resign. Therefore if Jane is more popular, she will be elected and Craig will resign.

J, E, C

3. The crop is good, but there is not enough water. If there is a lot of rain or not a lot of sun, then there is enough water. Therefore the crop is good and there is a lot of sun.

C, W, R, S

4. If the ad is successful, then the sales volume will go up. Either the ad is successful or the store will close. The sales volume will not go up. Therefore the store will close.

A, S, C

5. Russia was a superior power, and either France was not strong or Napoleon made an error. Napoleon did not make an error, but if the army did not fail, then France was strong. Hence the army failed and Russia was a superior power.

R, F, N, A

6. It is not the case that if electric rates go up, then usage will go down, nor is it true that either new power plants will be built or bills will not be late. Therefore usage will not go down and bills will be late.

R, U, P, B

7. If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed. Mr. Krasov was not in town. If a crime was committed, then Mr. Krasov was in town. Therefore Jose did not take the jewelry.

J, L, C, T

TABLE 1.14

 

More Inference Rules

 

From P -Q, Q -4 R

Can Derive P -> R

Name/Abbreviation for Rule Hypothetical syllogism-hs

P V Q, P"

Q

Disjunctive syllogism-ds

P -4 Q

Q"→ P"

Contraposition-cont

Q" -< P"

P → Q

Contraposition-cont

P

P A P

Self-reference-self

P V P

P

Self-reference-self

(P A Q) → R

P → (Q → R)

Exportation-exp

P, P"

Q

Inconsistency-inc

P A (Q V R)

(P A Q) V (P V R)

Distributive-dist

P V (Q V R)

(P V Q) V (P V R)

Distributive-dist

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Maurice Tutor
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Status NEW Posted 19 Sep 2017 12:09 PM My Price 10.00

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