Practice Exams

Here is a sample of the type of problems you will find on the final exam. Note that your exam will be a bit more difficult because we are not doing any predicate logic this term.

Logic Final Exam

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You are allowed to use any and all of the twenty rules that we have learned. Make sure that if you use IP or CP, that you indent properly!

Part One: Construct TWO proofs from the following list: (10 points each)

A]	1.	(C v D) É B
	2.	~B · A /\~D

B]	1.	(C v D) º (X · Y)
	2.	C /\Y

C]	1.	(~A v B)
	2.	B É C /\A É C

Part Two: Construct FOUR proofs from the following list: (15 points each)

A]	1.	(A v B) É ~(F · D)
	2.	~(A · ~D)
	3.	~F É ~(C · D) /\~(A · C)

B]	1.	X º ~Y
	2.	(Y v Z) É T
	3.	~(T v W) /\P É X

C]	Derive from no premises: ~((P º ~Q) · ~(P v Q))

D]	Derive from no premises: ~[(P É ~P) · (~P É P)]

E]	1.	(R · S) º (G · H)
	2.	R É S
	3.	H É G / \R º H

F]	1.	~(F · G) v ~(H · K)
	2.	(B · X) º ~K
	3.	~(X v Y)
	4.	~(H · F) É X /\~(G · A)

Part Three: Construct ONE proof from the following list: (10 points)

A]	1.	A É [(N v ~N) É (S v T)]
	2.	T É ~(F v ~F) / \ A É S

B]	1.	(X · Y) v ~(Z v W)
	2.	(Z · X) É (Y É ~B)
	3.	C É ~C
	4.	~(B v C) É ~Y /\ ~Z

Here are three recent midterm exams.

Logic Midterm #1

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A. True or False? (10 points)

1. _____ No valid argument can have a false conclusion.

2. _____ If p implies q and q implies p then they are equivalent.

3. _____ Any disjunction that contains a contradiction is itself a contradiction.

4. _____ If p, q, and r are the premises of an argument and the set of these are inconsistent, then the argument must be invalid.

5. _____ Conjoining a tautology with a contingent sentence always produces a tautology.

B. Wff or not? If not, correct it. (5 points)

1. ~ ~ (~A v B) · (S º R) v (Y É Q)

2. A ~ B

3. (a v b) º (a · D)

4. (((X v Y) · A) v (G Ì P))

5. Q = R

C. Long Truth Tables (20 points)

Construct truth tables for the following arguments. Then evaluate the arguments for validity. Be sure to show all work and to clearly indicate counterexamples, if any.

1. ~ (~Q · R)	1. ~ ~ Y · ~ ~ X
2. R	2. (X º Y) É ~Z
3. ~C É ~R	3. \ ~ (X v Z)
4. \ Q · C

D. Construct a truth table for these three sentences. (15 points)

1. D É (~A · B)

2. (B v ~A) É ~D

3. (A v C) º ~ (~C · ~A)

1. Are these three sentences consistent? Why/Why not? (5 points)

2. Does sentence one imply sentence two? Why/Why not? (5 points)

3. Does sentence three imply sentence one? Why/Why not? (5 points)

4. Are any of the sentences equivalent? Why/Why not? (5 points)

5. Of each of the sentences, determine if they are contingent, contradictory or tautologous. (10 points)

F. Construct an INDIRECT truth table to evaluate the following argument. (20 points)

1. (A º E) º ~C

2. ~ (~C É D)

3. ~D É E

4. \ ~C · A

BONUS: You do not have to do this question!!!! (10 points)

Using an INDIRECT truth table, determine if the following sentences are consistent:

1. ~ (A v (B v (C v D)))

2. A É (B É (C É D))

3. D v D

Hint: The key to this problem is in choosing what the initial truth values for the main operators must be. Consider what test is used for consistency and go from there.

Logic Midterm #2

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A. True or False? (10 points)

1. _____ A conjunction with a tautologous conjunct is never contingent.

2. _____ If p and q imply each other, q º p is a tautology.

3. _____ No set of consistent sentences can contain a tautology.

4. _____ No invalid argument can have a true conclusion.

5. _____ Two contingent sentences combined in a disjunction always produces a contradiction.

B. Wff or not? If not, correct it. (5 points)

1. ~ ~(( (~A · C) É D)

2. Q₄₁

3. (Q Ì R) º Y

4. ((Q v S) · (R º T) v (G v P))

5. (((P · R) · S) v ~Y) v ~ ~ ~ U

C. Long Truth Tables (20 points)

Construct truth tables for the following arguments. Then evaluate the arguments for validity. Be sure to show all work and to clearly indicate counterexamples, if any.

1. (A É ~A)	1. A É (B É A)
2. ~ (B v C)	2. ~ (~B v A)
3. \ B º C	3. ~A É (D · A)
	4. \ ~D

D. Construct a truth table for these three sentences. Note: All three sentences should be on the same table. (15 points)

1. D É (~A · B)

2. (~B v A) É ~D

3. (A v C) º (~C · ~A)

1. Are these three sentences consistent? Why/Why not? (5 points)

2. Does sentence one imply sentence two? Why/Why not? (5 points)

3. Does sentence three imply sentence one? Why/Why not? (5 points)

4. Are any of the sentences equivalent? Why/Why not? (5 points)

5. Of each of the sentences, determine if they are contingent, contradictory or tautologous. (10 points)

E. Construct an INDIRECT truth table to evaluate the following argument. (20 points)

1. A · (R É S)

2. (A v Y) É (Q · X)

3. Y É R

4. \ Q º S

BONUS: You do not have to do this question!!!! (10 points)

Using an INDIRECT truth table, determine if the following sentences are consistent:

1. (A v (B v (C v (D v E))))

2. (A º (B º (C º (D º E))))

3. (A · (B · (C · (D · E))))

Hint: The key to this problem is in choosing what the initial truth values for the main operators must be. Consider what test is used for consistency and go from there.

Midterm Exam for Logic 102 – Spring 99

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Section A. True or False. (5 points)

1. _____ If an argument is sound then that argument must be valid.

2. _____ A disjunction of two equivalent sentences is always a tautology.

3. _____ Every contradiction implies a tautology.

4. _____ It is possible for the conjunction of two contingent sentences to be a tautology.

5. _____ If p implies q and q implies r then p implies r.

Section B Wffs or not? If not, correct them. (5 points)

1. _____ ((Bº A) v (Qº C) v (Aº D))

2. _____ (~A, ~B, ~C)

3. _____ ~~(~(A v B))

4. _____ ~(((Q v C)))

5. _____ A É (A É A) É A

Section C Long Truth Tables (20 points)

Use graph paper! Construct truth tables for the following two arguments. Then, evaluate the arguments for validity. SHOW ALL WORK and clearly indicate counterexamples, if any.

1. A É ~(Q v R)	1. ~A É (~B · C)
2. (Q · ~A) · C	2. ~((A v ~C) v (~C v B))
3. \ R · C	3. \ B º A

Section D Truth Table Tests

Use graph paper! Show all work.

1. Construct a long truth table for the following wffs: (10 points)

(A · ~C) v Q

~Q É ~(~A v C)

~(A · ~C) · ~Q

2. Are these sentences consistent? Explain using truth table tests. (5 points)

3. Do any of the sentences imply the other? Explain. (10 points)

4. Are any of the sentences equivalent? Explain. (5 points)

5. Is the sentence ((A · ~C) v Q) º (~Q É ~(~A v C)) contingent, a tautology or a contradiction? (5 points)

6. Is the sentence ((A · ~C) v Q) º (~(A · ~C) · ~Q) contingent, a tautology or a contradiction? (5 points)

Section E Indirect Truth Tables (30 points)

Use graph paper! Use an indirect table to evaluate these two arguments for validity. Show all work and be sure to make clear counterexamples, if any.

1. (A v B) É ~Q	1. P v Q
2. (~Q º B) · (R v ~B)	2. P É (P É S)
3. (A v ~B) v Q	3. Q É (S É P)
4. \ R v S	4. \ P º S

Section F BONUS. You do not have to complete this section!

1. Use an INDIRECT truth table to test the following sentence for contingency, contradiction or tautology. (Hint: It’s not as easy as it seems. Consider the truth table tests that are required.) (5 points)

A v B