Reference no: EM132290956

Ethics and Society Assignment -

Translation Questions 1-5: Translate the following statements into symbolic form using the text symbols for truth functional connectives, and upper case letters to represent affirmative ordinary language statements. Clearly indicate the simple statements you are symbolizing and the symbol you are using to symbolize them.

1. Neither the President nor the Prime Minister will make any concessions.

2. Only Richard and Fred were caught by the police.

3. Bonnie will steal only if Clyde robs banks and grocery stores.

4. The department stores will raise their prices if either the cost of manufacturing increases or the clerks don't agree to a settlement.

5. Although the executives are opposed to our plan, they will help us if they do not find anyone who will contribute money.

6. Construct a truth table for the following statement. Indicate whether the statement is a tautology, a contradiction, or a contingent statement. Do not use any shortcuts in the table. After completing your truth table explain how it indicates your answer. (10 marks)

(A ⊃ A) ⊃ [B • (C • ∼ C)]

7. Construct a truth table to determine whether the following pair of statements are logically equivalent. Do not use any shortcuts in the table. After completing your truth table explain how it indicates your answer.

(C • D) ⊃ ∼ D

C v ∼D

8. Construct a truth table to determine whether the following argument is valid or invalid. Do not use any shortcuts in your truth table. After completing your truth table explain how it indicates your answer.

1) ∼A

2) A v B

3) B ⊃ C

C

Proof Questions 9-12: Provide a formal proof of validity of the following arguments. For 9, and 10 you may use CP, or IP, in addition to any of the 18 rules of inference. For 11 you must use CP, and for 12 you must use IP.

9.

1) R

2) (∼ C v ∼ D) v S

3) ∼ (C • D) ⊃ ∼ R / S

10.

1) (A • B) ⊃ ∼ (S v T)

2) ∼E

3) (S v T) v ∼ (∼E • ∼F)

4) (∼E v F) ⊃ (A •B) / E v F

11.

1) A ⊃ B /  A ⊃ [ C ⊃ ∼ (B ⊃ ∼A) ]

12.

1) A v B

2) B ⊃ (A v D)

3) ∼ D / A

13. Symbolize the following argument, using symbolized statements and the relevant truth-functional connectives. Indicate the upper case letters you use to symbolize ordinary language simple statements. Determine whether the argument is valid or invalid. In order to do that, you may construct a complete truth table, use the indirect method, or construct a formal proof of validity.

If the cube was soluble and it dissolved, then it was placed in liquid. If the cube dissolved if and only if it was placed in liquid, then it was soluble. Therefore, if the cube was soluble if and only if it dissolved, then it was placed in liquid.

References -

1. Baronett, Stan. Logic Second Edition. OUP. (New York: 2013) ISBN 978-0-19-984631-3.

2. Flage, Daniel E.. Understanding Logic. Prentice-Hall. (Englewood Cliffs New Jersey: 1995) ISBN 0-02-338173-6.

3. Salmon, Merrilee H.. Introduction to Logic and Critical Thinking Third Edition. Harcourt Brace & Company. (Fort Worth: 1995) ISBN 0-15-543064-5.

4. Warmbrod, Ken. Logic and Philosophy of Logic Course Guide for Philosophy 2430. University of Manitoba. (Winnipeg: 2013) ISBN 978-0-200-00202-8.