Introduction to Sentential Logic

INTRODUCTION TO SENTENTIAL LOGIC EXERCISE

SYMBOLIZING IN SENTENTIAL LOGIC Part I Using the dictionary provided, symbolize the following claims in Sentential Logic.

1. Either professors do not accept late homework submissions or, if you have a legitimate excuse that you tell them in advance, then professors give you a break. A -- Professors accept late homework submissions. E -- You have a legitimate excuse that you tell them in advance. B -- Professors will give you a break.

~A V (E  B)

2. The students in my high school class in Venezuela could relax and party at the drop of the hat. If you can relax at the drop of the hat you tend not to abuse drugs as much. The students in my high school class in Venezuela tended not to abuse drugs as much. R -- The students in my high school class in Venezuela could relax at the drop of a hat. P -- The students in my high school class in Venezuela could party at the drop of a hat. D – Venezuelans are great dancers. A – You tend to abuse drugs as much.

R & P R  ~A ~A

Part II Symbolize the following claims in Sentential Logic, making up and providing a dictionary of terms.

3. Blanca Molina had to make up her brother’s bed every day. In Venezuela women are supposed to wait on men and take care of them.

1 M -- Blanca Molina had to make up her brother’s bed every day W -- In Venezuela women are supposed to wait on men. C -- In Venezuela women are supposed to take care of men.

M W & C

4. Liliana Montico thought that all Americans were spoiled and that all Venezuelans were not. If Liliana Montico thought all Americans were spoiled she had a lot of stereotypes. Therefore, Liliana Montico had a lot of stereotypes.

A – Liliana Montico thought all Americans were slutty. V – Liliana Montico thought that all Venezuelans were slutty. S -- Liliana Montico had a lot of stereotypes.

A & ~V A  S S

5. Either Liliana Montico was right or not right in her stereotypes. If most Americans thought Venezuelans are inferior then most Americans are not right. Most Americans thought Venezuelans were inferior. Therefore, most Americans were not right and Liliana Montico was either right or wrong.

Dictionary provided above, plus the following additional entries

R – Liliana Montico was right in her stereotypes. I – Most Americans thought Venezuelans are inferior. C – Most Americans were right

R V ~R I  ~C I ~C & (R V ~R)

6. If you take the right classes from a community college and transfer to CSUS you can get credit for most of your classes. You took the right

2 classes and transferred from a community college to CSUS. You should get credit for most of your classes.

R – You take the right classes from a community colleges. T – You transfer to CSUS. C – You can get credit for most of your classes

(R & T)  C R & T C

7. All Carolina Landaez’s classmates visited her in the hospital. If all Carolina Landaez’s classmates visited Carolina Landaez in the hospital they either cared about her or liked to look good to the priest. If you look good to the priest and go to confession regularly you will get a good grade and into heaven. All Carolina’s classmates went to confession regularly. Therefore, all Carolina’s classmates will get into heaven.

V -- All Carolina Landaez’s classmates visited her in the hospital. C -- All Carolina Landaez’s classmates cared about her. L -- All Carolina Landaez’s classmates liked to look good to the priest. R – You go to confession regularly. G – You will get a good grade. H – You will get into heaven.

V V  (C V L) (L & R)  (G & H) H

REPRESENTING SENTENCES IN TRUTH TABLES

Represent each of sentences 1, 3 and 4 above on separate truth tables and identify the logical properties of each.

8. (1 above)

~A V (E  B)

3 A B E ~A E  B ~A V (E  B) T T T F T T T T F F T T T F T F F F T F F F T T F T T T T T F T F T T T F F T T F T F F F T T T

Contingent (see row 3)

9. (3 above)

M W & C

M T contingent F

C W W & C T T T T F F F T F F F F contingent

10. (4 above)

A & ~V A  S S

A V ~V A & ~V

4 T T F F T F T T F T F F F F T F contingent

A S A  S T T T T F F F T T F F T contingent

S T contingent F

USING TRUTH TABLES TO SEE WHETHER AN ARGUMENT IS VALID Represent each of sentences 5 and 6 above on truth tables and use the tables to determine whether the argument is VALID.

11. (5 above)

R V ~R I  ~C I ~C & (R V ~R) P1 P2 P3 Conclusion C I R ~R ~C R V ~R I I  ~C ~C & (R V ~R) T T T F F T T F F T T F T F T T F F T F T F F T F T F T F F T F T F T F F T T F T T T T T F T F T T T T T T F F T F T T T T T F F F T T T T T T

5 Valid, no rows with TTTF

12. (6 above)

(R & T)  C R & T C

P1 P2 P3 Conclusion C R T R & T (R & T)  C R & T C T T T T T T T T T F F T F T T F T F T F T T F F F T F T F T T T F T F F T F F T F F F F T F T F F F F F F T F F