Introductory Logic Unit 3 - Assignment 4 50 Pts. I. Translate each of the follow

Question

Introductory Logic

Unit 3 - Assignment 4

50 Pts.

I. Translate each of the following simple and complex English sentences into a claim of propositional logic. Write your translation underneath the English sentence.If the claim is complex, also identify the major operator.(3 pts. each)

1. It is either a cat or a skunk.

2. It flies.

3. If it flies, it is either a bird or a plane.

4. It looks very strange for a bird or plane.

5. Either it is a bird and it is deformed or it is a plane and it’s very small.

6. If it is a bird and it is deformed, then someone either burned it or painted it.

7. It is not a plane.

8. If someone burned it, it would not be hopping around so happily.

9. It is hopping around happily.

10. If it was not burned, then someone must have painted it.

II. Using the interpretations provided, translate the following claims of propositional logic into English. Write your answers underneath. (2 pts. each)

1. [T = I throw the ball; W = The window will break.]                 

(T à W)

2. [R = You’re a Republican; D = You’re a Democrat.]

(((R v D) &¬R) à D)

3. [R = It is raining; S = The sidewalks are wet.]

(((R à S) & R) à S)

4. [S = It snowed; R = The roof collapsed.]

(((S à R) &¬R) à¬S)

5. [R = It is raining; B = I bring my umbrella; W = I get wet.]

((R &¬B) à W)

6. [B = The dog will bite; F = The dog is friendly; P = I will pet the dog.]

((B v F) & ((F à P) & (Bà¬P)))

7. [P = I pay for the ticket; K = I get kicked out.]

(¬(¬P à K) à¬P)

8. [P = I am a professor; D = I have a Ph.D.; T = I have teaching experience.]

(P (D & T))

9. [P = He went to the park; R = He went to the restaurant; S = He is on the swings; J = He is on the jungle gym.]

((P v R) & ((P à (S v J)))

10. [D = She is a (medical) doctor; M = She went to medical school; L = She is licensed; I = She is immoral; H = She is a hack.]

((D M) & (¬L à (I v H)))

Explanation / Answer

1. S. It is a cat R. it is a skunk.

3. S. It can fly R. It is a bird. T. It is a plane.

4. S. Is this a plane or bird. R. It looks strange.

5. S. This is a bird. R. It looks deformed. T. It is a plane. Q. It looks small.   

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