TEST BANK
UNIT 1
SECTION 2
1. In the context of logic, what is an argument?
2. What aspect of arguments does logic examine?
3. What is a premise?
4. Which of the following are arguments?
a. John likes Mary, but Mary doesn’t like John.
b. John likes Mary, so if she doesn’t like him, he will be unhappy.
c. John will get an A in logic, since he studies hard and never misses class.
5. For the following arguments, state the premises and the conclusion.
a. We did not have a late freeze, so there will be a good apple crop, since there
was plenty of rain.
b. The cat must be ill. She is not eating and she sleeps all day.
c. My tulips have been eaten, so there are probably deer or rabbits in the area.
SECTIONS 3 – 4
1. What is the difference between an inductive and a deductive argument?
2. What does it mean for an argument to be valid?
3. What does it mean for an argument form to be valid?
4. Can a valid argument have a false premise?
5. What is a counter-example to an argument form?
UNIT 2
SECTION 1
1. What is a compound sentence?
2. What is a simple sentence?
3. Are the following simple or compound?
a. Andrew likes skiing but not snowboarding.
b. The last person to leave the building at night should turn out the lights on the
main floor.
c. People don’t trust liars.
4. Are the following simple or compound?
a. John and Mary like bridge.
b. John and Mary are bridge partners.
c. Andrew does not play golf or billiards.
5. Are the following simple or compound?
a. Puppies and kittens are irresistible.
b. Kittens aren’t mean.
c. The kitten that John gave to Mary is very playful in the wee hours of morning.
1
,SECTIONS 2 – 3
1. What is a sentential operator?
2. What are the components of a conditional called?
3. What are the components of conjunctions and disjunctions called?
4. What is the major operator of the following?
a. (~ (~ A v ~ C) ⊃ ~ D)
b. (((A v B) . (A v C)) ≡ (A v (B . C))
c. ~ (((A . B) v (C . D)) . ((A ≡ B) v (C ≡ D)))
5. What is the major operator of the following?
a. (((A ⊃ B) . C) v ((C ≡ (B v A)) ⊃ A))
b. ((((A ⊃ B) . C) v (C ≡ (B v A))) ⊃ A)
c. (((~ (~ A v B) ⊃ ~ (B v A)) ≡ ~ (~ A v ~ B)) ⊃ B)
6. What is the major operator of the following?
a. (~ ((G ⊃ G) ⊃ (~ G ⊃ G)) . (G v ~ G))
b. (((A v B) v (C v D)) . ((A . B) . (C v D)))
c. (((~ A ≡ (C ⊃ D)) . (~ B ≡ (~ D ⊃ C))) v (C ⊃ ~ D))
UNIT 3
SECTION 1
1. Write down the truth table for the following operator and explain in English what the
table means.
a. v c. ⊃ e. .
b. ~ d. ≡
SECTION 2
1. Given that A, B, and C are true and X, Y, and Z are false, compute the value of the
following.
a. ~ (~ A v ~ X)
b. ~ (A ≡ ~ B) ⊃ ~ (~ Y ≡ ~ C)
c. ((A . X) v (B . ~ Y)) ⊃ (~ B ≡ ~ Y)
2. Given that A, B, and C are true and X, Y, and Z are false, compute the value of the
following.
a. ~ (B . ~ C)
b. ~ (A ≡ ~ X) ≡ ~ (Y ≡ ~ B)
c. ~ ((A v X) . (Y v ~ B)) ⊃ ~ (~ A v ~ Y)
3. Are the following true or false?
a. If the antecedent of a conditional is false, then the conditional is always true.
b. If the consequent of a conditional is false, then the conditional is always false.
c. If one conjunct is false, that guarantees that the conjunction will be false.
4. Are the following true or false?
a. If the antecedent of a conditional is true, then the truth value of the conditional
will be the same as the truth value of the consequent.
b. The biconditional is false in only one row of its truth table.
c. One true disjunct guarantees the truth of a disjunction.
2
,SECTIONS 3 – 4
1. What does it mean for an operator to be truth functional?
2. Give two examples of non-truth-functional operators.
3. How would we demonstrate that an operator is not truth functional?
4. Are our five operators the only ones that are truth functional? If so, explain why. If
not, give an example of another.
UNIT 4
SECTIONS 1 – 3
1. Are the following true or false?
a. An appropriate symbolization for “I won’t go to the party” would be ‘P’.
b. “Neither A nor B” can be symbolized as ~ (A v B).
c. “Not both A and B” can be symbolized as (~ A . ~ B).
d. “B only if not A” can be symbolized as (~ A ⊃ B).
e. “A unless B” can be symbolized as (A v B) or as (~ B ⊃ A).
2. Which of the following are truth-functionally compound?
a. Jack and Jill went up the hill.
b. Jack went up the hill because he needed a pail of water.
c. Jack didn’t make it down the hill safely.
d. Jill came tumbling down after Jack tumbled down.
e. Jack’s mother asked him to get a big pail of water from the top of the hill.
3. Are the following true or false?
a. “Ajax is a cat” is a sufficient condition for “Ajax is a mammal”.
b. “Ajax is a feline” is a necessary condition for “Ajax is a kitten”.
c. “Ajax is a cat” is a sufficient condition for “Ajax is not a dog”.
d. “Ajax is a cat” is a necessary condition for “Ajax is not a dog”.
e. “John won the lottery” is a sufficient condition for “John had a lottery ticket”.
SECTION 4
1. Symbolize the following, using the indicated abbreviations.
L = The locusts will kill my trees; C = I cover my trees; B = The rabbits will kill my
trees; F = I feed my trees; W = I water my trees; Y = My trees turn yellow; R = It
rains; D = My trees look droopy; A = My trees produce great apples; Z = There is a
hard freeze.
a. The locusts will kill my trees unless I cover them.
b. I will either feed or water my trees, but not both.
c. Neither the locusts nor the rabbits will kill my trees if I feed and water them.
d. I will feed my trees only if they turn yellow, and I will water them only if it
doesn’t rain and they look droopy.
e. My trees will produce great apples if I feed and water them and they are not killed
by the locusts, unless they are killed by the rabbits or there is a hard freeze.
3
, 2. Symbolize the following, using the indicated abbreviations.
L = John will lose his license; I = John loses his insurance; A = John will have an
accident; M = John sells his motorcycle; H = John ends up in the hospital; C = John is
convicted of careless driving; U = John is convicted of DUI; Q = John quits speeding.
a. John will have an accident and lose his license and insurance if he doesn’t sell
his motorcycle.
b. John will sell his motorcycle only if he either loses his license or has an
accident and ends up in the hospital.
c. If John doesn’t sell his motorcycle and quit speeding, then he will end up in the
hospital if and only if he has an accident and is convicted of careless driving.
d. If John has an accident he will not lose both his insurance and his license
unless he is convicted of careless driving or DUI.
e. If John doesn’t quit speeding, he will have an accident, lose his insurance, and
end up in the hospital, unless he is convicted of careless driving or DUI and
loses his license.
3. Symbolize the following, using the indicated abbreviations.
R = John will get a raise; W = John works hard; I = John insults his boss; Q = John
quits; P = John gets a promotion; B = the company goes bankrupt; D = John will be
discouraged; M = John will be motivated.
a. John will get a raise if he works hard and doesn’t insult his boss.
b. John will quit if and only if he does not get both a raise and a promotion.
c. John will get neither a raise nor a promotion only if he either insults his boss
or doesn’t work hard.
d. If John doesn’t quit he will get a raise and a promotion if he works hard,
unless he insults his boss or the company goes bankrupt.
e. If John doesn’t get either a raise or a promotion, he will be unmotivated and
won’t work hard, but he won’t quit unless he is discouraged or insults his boss.
UNIT 5
1. What is a valid argument form? A counter-example?
2. Are the following true or false?
a. A counter-example always has true premises and a false conclusion.
b. An invalid argument always has a false conclusion.
c. There are 16 rows in the truth table for (p ⊃ (q v ~ r)) v ((q . ~ p) ⊃ (s . ~ t)).
d. A truth table may have 48 rows.
3. Use the truth table method to determine whether the following are valid or invalid.
Show your work and be explicit in your answer.
a. (p v q) ⊃ ~ q, (p v q) ⊃ ~ p /.. ~ (p v q)
b. (p v q) ⊃ (q ≡ ~ r), p ≡ (r . ~ q) /.. (~ p v ~ q) ⊃ r
c. p ⊃ (~ q v ~ r), r ⊃ p /.. r ⊃ ~ q
d. p ⊃ (q . r), ~ p ⊃ ~ (q v r) /.. p ≡ (q v r)
4
UNIT 1
SECTION 2
1. In the context of logic, what is an argument?
2. What aspect of arguments does logic examine?
3. What is a premise?
4. Which of the following are arguments?
a. John likes Mary, but Mary doesn’t like John.
b. John likes Mary, so if she doesn’t like him, he will be unhappy.
c. John will get an A in logic, since he studies hard and never misses class.
5. For the following arguments, state the premises and the conclusion.
a. We did not have a late freeze, so there will be a good apple crop, since there
was plenty of rain.
b. The cat must be ill. She is not eating and she sleeps all day.
c. My tulips have been eaten, so there are probably deer or rabbits in the area.
SECTIONS 3 – 4
1. What is the difference between an inductive and a deductive argument?
2. What does it mean for an argument to be valid?
3. What does it mean for an argument form to be valid?
4. Can a valid argument have a false premise?
5. What is a counter-example to an argument form?
UNIT 2
SECTION 1
1. What is a compound sentence?
2. What is a simple sentence?
3. Are the following simple or compound?
a. Andrew likes skiing but not snowboarding.
b. The last person to leave the building at night should turn out the lights on the
main floor.
c. People don’t trust liars.
4. Are the following simple or compound?
a. John and Mary like bridge.
b. John and Mary are bridge partners.
c. Andrew does not play golf or billiards.
5. Are the following simple or compound?
a. Puppies and kittens are irresistible.
b. Kittens aren’t mean.
c. The kitten that John gave to Mary is very playful in the wee hours of morning.
1
,SECTIONS 2 – 3
1. What is a sentential operator?
2. What are the components of a conditional called?
3. What are the components of conjunctions and disjunctions called?
4. What is the major operator of the following?
a. (~ (~ A v ~ C) ⊃ ~ D)
b. (((A v B) . (A v C)) ≡ (A v (B . C))
c. ~ (((A . B) v (C . D)) . ((A ≡ B) v (C ≡ D)))
5. What is the major operator of the following?
a. (((A ⊃ B) . C) v ((C ≡ (B v A)) ⊃ A))
b. ((((A ⊃ B) . C) v (C ≡ (B v A))) ⊃ A)
c. (((~ (~ A v B) ⊃ ~ (B v A)) ≡ ~ (~ A v ~ B)) ⊃ B)
6. What is the major operator of the following?
a. (~ ((G ⊃ G) ⊃ (~ G ⊃ G)) . (G v ~ G))
b. (((A v B) v (C v D)) . ((A . B) . (C v D)))
c. (((~ A ≡ (C ⊃ D)) . (~ B ≡ (~ D ⊃ C))) v (C ⊃ ~ D))
UNIT 3
SECTION 1
1. Write down the truth table for the following operator and explain in English what the
table means.
a. v c. ⊃ e. .
b. ~ d. ≡
SECTION 2
1. Given that A, B, and C are true and X, Y, and Z are false, compute the value of the
following.
a. ~ (~ A v ~ X)
b. ~ (A ≡ ~ B) ⊃ ~ (~ Y ≡ ~ C)
c. ((A . X) v (B . ~ Y)) ⊃ (~ B ≡ ~ Y)
2. Given that A, B, and C are true and X, Y, and Z are false, compute the value of the
following.
a. ~ (B . ~ C)
b. ~ (A ≡ ~ X) ≡ ~ (Y ≡ ~ B)
c. ~ ((A v X) . (Y v ~ B)) ⊃ ~ (~ A v ~ Y)
3. Are the following true or false?
a. If the antecedent of a conditional is false, then the conditional is always true.
b. If the consequent of a conditional is false, then the conditional is always false.
c. If one conjunct is false, that guarantees that the conjunction will be false.
4. Are the following true or false?
a. If the antecedent of a conditional is true, then the truth value of the conditional
will be the same as the truth value of the consequent.
b. The biconditional is false in only one row of its truth table.
c. One true disjunct guarantees the truth of a disjunction.
2
,SECTIONS 3 – 4
1. What does it mean for an operator to be truth functional?
2. Give two examples of non-truth-functional operators.
3. How would we demonstrate that an operator is not truth functional?
4. Are our five operators the only ones that are truth functional? If so, explain why. If
not, give an example of another.
UNIT 4
SECTIONS 1 – 3
1. Are the following true or false?
a. An appropriate symbolization for “I won’t go to the party” would be ‘P’.
b. “Neither A nor B” can be symbolized as ~ (A v B).
c. “Not both A and B” can be symbolized as (~ A . ~ B).
d. “B only if not A” can be symbolized as (~ A ⊃ B).
e. “A unless B” can be symbolized as (A v B) or as (~ B ⊃ A).
2. Which of the following are truth-functionally compound?
a. Jack and Jill went up the hill.
b. Jack went up the hill because he needed a pail of water.
c. Jack didn’t make it down the hill safely.
d. Jill came tumbling down after Jack tumbled down.
e. Jack’s mother asked him to get a big pail of water from the top of the hill.
3. Are the following true or false?
a. “Ajax is a cat” is a sufficient condition for “Ajax is a mammal”.
b. “Ajax is a feline” is a necessary condition for “Ajax is a kitten”.
c. “Ajax is a cat” is a sufficient condition for “Ajax is not a dog”.
d. “Ajax is a cat” is a necessary condition for “Ajax is not a dog”.
e. “John won the lottery” is a sufficient condition for “John had a lottery ticket”.
SECTION 4
1. Symbolize the following, using the indicated abbreviations.
L = The locusts will kill my trees; C = I cover my trees; B = The rabbits will kill my
trees; F = I feed my trees; W = I water my trees; Y = My trees turn yellow; R = It
rains; D = My trees look droopy; A = My trees produce great apples; Z = There is a
hard freeze.
a. The locusts will kill my trees unless I cover them.
b. I will either feed or water my trees, but not both.
c. Neither the locusts nor the rabbits will kill my trees if I feed and water them.
d. I will feed my trees only if they turn yellow, and I will water them only if it
doesn’t rain and they look droopy.
e. My trees will produce great apples if I feed and water them and they are not killed
by the locusts, unless they are killed by the rabbits or there is a hard freeze.
3
, 2. Symbolize the following, using the indicated abbreviations.
L = John will lose his license; I = John loses his insurance; A = John will have an
accident; M = John sells his motorcycle; H = John ends up in the hospital; C = John is
convicted of careless driving; U = John is convicted of DUI; Q = John quits speeding.
a. John will have an accident and lose his license and insurance if he doesn’t sell
his motorcycle.
b. John will sell his motorcycle only if he either loses his license or has an
accident and ends up in the hospital.
c. If John doesn’t sell his motorcycle and quit speeding, then he will end up in the
hospital if and only if he has an accident and is convicted of careless driving.
d. If John has an accident he will not lose both his insurance and his license
unless he is convicted of careless driving or DUI.
e. If John doesn’t quit speeding, he will have an accident, lose his insurance, and
end up in the hospital, unless he is convicted of careless driving or DUI and
loses his license.
3. Symbolize the following, using the indicated abbreviations.
R = John will get a raise; W = John works hard; I = John insults his boss; Q = John
quits; P = John gets a promotion; B = the company goes bankrupt; D = John will be
discouraged; M = John will be motivated.
a. John will get a raise if he works hard and doesn’t insult his boss.
b. John will quit if and only if he does not get both a raise and a promotion.
c. John will get neither a raise nor a promotion only if he either insults his boss
or doesn’t work hard.
d. If John doesn’t quit he will get a raise and a promotion if he works hard,
unless he insults his boss or the company goes bankrupt.
e. If John doesn’t get either a raise or a promotion, he will be unmotivated and
won’t work hard, but he won’t quit unless he is discouraged or insults his boss.
UNIT 5
1. What is a valid argument form? A counter-example?
2. Are the following true or false?
a. A counter-example always has true premises and a false conclusion.
b. An invalid argument always has a false conclusion.
c. There are 16 rows in the truth table for (p ⊃ (q v ~ r)) v ((q . ~ p) ⊃ (s . ~ t)).
d. A truth table may have 48 rows.
3. Use the truth table method to determine whether the following are valid or invalid.
Show your work and be explicit in your answer.
a. (p v q) ⊃ ~ q, (p v q) ⊃ ~ p /.. ~ (p v q)
b. (p v q) ⊃ (q ≡ ~ r), p ≡ (r . ~ q) /.. (~ p v ~ q) ⊃ r
c. p ⊃ (~ q v ~ r), r ⊃ p /.. r ⊃ ~ q
d. p ⊃ (q . r), ~ p ⊃ ~ (q v r) /.. p ≡ (q v r)
4
