Answers

Here is my answer key. I am fairly certain that there are no errors but this remains a possibility. If you find one, email me. Also, you can use the class email to have a virtual study session. Just hit 'reply to all' on the email I sent and you can ask questions/give advice to all of the other students.

As you can see, the formatting is not the best. This occurs because when I convert from Word to HTML.

Sorry.

Answers for Practice Exams

Exam #1

Part A

1. F

2. T

3. F

4. F

5. F

Part B

1. Not wff: ~~(A v B) ((S º R) v (Y É Q))

2. Not wff: A v ~B

3. Not wff: (a v b) º (a · d)

4. Not wff: (((X v Y) · A) v (G É P))

5. Not wff: Qº R

Part C

Valid, no counterexample

Z))

Invalid, counterexample on row 2

Part D

1. Consistent, in row 2, all sentences are T

2. No implication, counterexample in row 9

3. No implication, counterexample in row 1

4. No, none have identical truth values in all rows.

5. 1,2 are contingent. 3 is a tautology.

Part F

Valid, contradiction occurs in conclusion.

BONUS: A question like this will appear on the final for the bonus. Try to figure out how this would be solved.

Exam #2

For exams 2 and 3, I have abbreviated the answers. On the exam, you must show all work!

Part A

1. F

2. T

3. F

4. F

5. F

Part B

1. Not wff: ~~((~A · C) É D)

2. Wff

3. Not wff: (Q É R) º Y

4. Not wff: (((Q v S) · (R º T)) v (G v P))

5. Wff

Part C

Both arguments are valid.

Part D

(~A · B)

(~B v A)

(A v C)

(~C · ~A)

1. No, there is no row where all the sentences are True.

2. Yes, there is implication because there is no row where 1 is T but 2 is false.

3. Yes, there is implication because there is no row where 3 is T but 1 is false.

4. 1 and 2 are equivalent because they have the same truth values in every row.

5. 1, 2 are contingent, 3 is a contradiction.

Part E

Invalid where A=T, Q=T, R=F, S=F, X=T, Y=F

Exam #3

Part A

1. T

2. F

3. T

4. F

5. T

Part B

1. Not wff: (((B º A) v (Q º C)) v ( A º D))

2. Not wff: ((~A · ~B) · ~C)

3. Not wff: ~~~(A v B)

4. Not wff: ~(Q v C)

5. Not wff: (A É (A É A)) É A

Part C

First argument is invalid: A=F, C=T, Q=T, R=F.

Second argument is valid.

Part D

(A · ~C)

~(~A v C)

~(A · ~C)

2. Not consistent because there are no rows in the table where all three sentences are T.

3. 1 implies 2 and 2 implies 1 because they are equivalent. (Or there are no rows where 1 is T and 2 is F or where 2 is T and 1 is F.

4. Yes, 1 and 2 are equivalent because they have the same truth value in every row.

5. Tautology

6. Contradiction

Part E

Invalid where A=F, B=F, Q=T, R=F, S=F

Valid: Contradiction occurs in row 1 in second premise. Contradiction occurs in row 2 in first premise.