06 Dec PHIL 117 EXAM #2 Directions: Download this exam and answer

PHIL 117 EXAM #2

Directions: Download this exam and answer the questions using your word processing software. You may print it, fill it in by hand, and then scan it if you’d like. If you do so, be sure that all answers are legible. When you are finished, please upload the exam to Canvas as either an MSWord document (.docx) or Adobe document (.pdf). Be sure you have answered all of the questions as thoroughly as needed, as per the directions in each section. You will have the full class session to finish. If you use out-of-class sources to answer questions, you must cite the sources you have used. The test is worth 200 points.

 

True/False Questions (20 points total): Indicate whether the following statements are true or false.

1. Some statements are valid. ________________________________________________________

2. Valid arguments must have true conclusions. ________________________________________________________

3. If an argument has a false conclusion, then it must be invalid. ________________________________________________________

4. The complete truth table for three distinct variables has 8 rows. ________________________________________________________

5. If the antecedent of a conditional statement is false, then the conditional must be true. ________________________________________________________

6. There may be more than one minor logical operator in a statement. ________________________________________________________

7. On a completed truth table, the column under the main operator of a symbolic expression indicates the truth value for that expression.

________________________________________________________

 

8. A well-formed formula (WFF) is always grammatically correct and never vague.

________________________________________________________

 

 

9. The following statement is a well-formed formula: ∼[P ⦁ ∼(∼∼Q → R ⌵ S)].

________________________________________________________

 

 

 

10. If the form of an argument is valid, then all arguments with that form will be valid.

________________________________________________________

 

Short Answer Questions (30 points total): Write your answer to the following questions. As a rule of thumb, answers may be as short as a single word, but shouldn’t need to be longer than four sentences.

1. What is the definition of validity?

 

 

 

 

2. What are the two conditions necessary for an argument to be sound?

 

 

 

 

3. Under what conditions is the biconditional operator true?

 

 

 

 

 

4. Under what conditions is the conditional operator false?

 

 

 

 

 

5. Under what conditions is the disjunction operator false?

 

 

 

 

 

6. Under what conditions is the conjunction operator true?

 

 

 

 

 

7. Provide the truth table for the negation operator, using the variable “P”.

 

 

 

 

 

 

8. Explain what it means for a statement to be a tautology and provide an example of a tautological statement.

 

 

 

 

 

 

9. Explain what it means for a statement to be a contradiction and provide an example of a contradictory statement.

 

 

 

 

 

 

10. Explain what it means for a statement to be contingent and provide an example of a contingent statement.

 

 

 

 

 

 

 

 

 

Exercises Section 1 – Symbolizing English Sentences (30 points total): Provide the symbolic form of the arguments below using variables of your choice. (DO NOT CONSTRUCT A TRUTH TABLE. YOU DO NOT NEED TO INDICATE VALIDITY.)

You may copy and paste the following symbols for your truth tables: Negation: ∼ Disjunction: ⌵ Conjunction: ⦁ Conditional: → Biconditional: ↔

1. If Grover Cleveland was the 22nd president of the United States and also the 24th president of the United States, then he served non-consecutive terms in office. Grover Cleveland was the 22nd president of the United States and also the 24th president of the United States. So, Grover Cleveland served non-consecutive terms in office.

 

 

 

2. If Susan is either extraordinarily talented or extraordinarily motivated, then she will receive a 4.0 at Yale. It’s false that Susan is extraordinarily motivated, but she is extraordinarily talented. So, Susan will receive a 4.0 at Yale.

 

 

 

3. Either Smith or Jones has four coins in their pocket. Smith has four coins in his pocket if and only if Cathy paid him on time. Jones has four coins in his pocket if and only if Barbara paid him on time. So, either Cathy paid Smith on time, or Barbara paid Jones on time.

 

 

 

4. We are either alive, or we are not alive. If we are alive, then we do not experience death. If we are not alive, then it’s not the case that we have experiences. If it’s not the case that we have experiences, then we do not experience death. So, either we do not experience death or we do not experience death.

 

 

 

5. Modern science is capable of genetically modifying brain cells to activate when stimulated with light. If this is true, and we had some way to disperse the modified genes through the gene pool, then this technology could be used to effectively mind control people through their television sets. Thus, if we had some way to disperse the modified genes through the gene pool, we could take over the world or we could go eat some burritos at Casa.

 

 

 

 

 

Exercises Section 2 – Truth Tables for Statement Types (40 points total): Complete the following two steps. First, construct a complete truth table for the following symbolic statements. Second, indicate whether the statement is a tautology, a contradiction, or contingent.

 

1. P → ∼P

 

 

 

 

2. ∼(T ⦁ ∼T) ⌵ S

 

 

 

 

 

 

 

3. (∼A ⌵ B) ↔ (A → B)

 

 

 

 

 

 

 

 

4. [(P ⦁ Q) ⌵ ∼P] → Q

 

 

 

 

 

 

 

 

 

5. ∼[(P ⦁ R) → (R ⌵ ∼R)]

 

 

 

 

 

 

 

 

 

 

Exercises Section 3 – Truth Tables, Arguments, and Validity (40 points total): Complete the following steps. First, construct a complete truth table for the following arguments. Then indicate whether the argument is valid or invalid. If it is invalid, write the truth values for the atomic statements that show the argument to be invalid. You may use additional paper. If you do so, please be sure to clearly mark which question you are answering.

1.

1. P ⦁ Q

2. ∴ P → Q

 

 

 

 

 

 

 

 

 

2.

1. P ↔ (P ⌵ ∼Q)

2. ∼Q

3. ∴ P

 

 

 

 

 

 

 

 

 

 

3.

1. ∼(A ⌵ ~B)

2. C → B

3. ∴ ∼(C ⌵ A)

 

 

 

 

 

 

 

 

 

 

 

 

 

4.

1. A → (B ⦁ C)

2. B ↔ (∼C → ∼B)

3. ∴ ∼B ⦁ C