Deck 8: Reasoning With Syllogisms

Question 1

The form of a disjunctive proposition is:

A)p or q
B)p and q
C)if p, then q
D)unless p, q
E)p, not q

Answer 1

A

Question 2

Suppose that p is the proposition "No one-story house has an interior staircase." What is the proposition not-p?

A)Some one-story houses do not have interior staircases.
B)Some one-story houses have interior staircases.
C)No house with an interior staircase is one story.
D)All one-story houses have interior staircases.
E)All houses with interior staircases are one story.

Answer 2

B

Question 3

Not (p and q) means that p and q cannot both be true.This is equivalent to:

A)p or q
B)not-p or not-q
C)p or not-q
D)not-p or q
E)p

Answer 3

B

Question 4

The proposition p and the proposition not-p are:

A)contraries
B)subcontraries
C)contradictories
D)contrapositives
E)converses

Question 5

If p is a categorical proposition with negative quality, then not-p must be:

A)negative
B)universal
C)particular
D)a double negative, which is equivalent to a universal negative
E)a double negative, which is equivalent to an affirmative

Question 6

Suppose that p is the proposition "It is not snowing." Which of the following propositions would be equivalent to not-p?

A)It will snow later.
B)It was snowing.
C)It is sunny.
D)It is snowing.
E)It may or may not be snowing.

Question 7

When we write out the logical form of a compound proposition, the letters p and q are used to represent:

A)subject and predicate, respectively
B)predicate and subject, respectively
C)concepts
D)connectives
E)complete propositions

Question 8

In the inclusive sense, "p or q" means:

A)p or q, but not both
B)p or q, or both
C)p or q, or neither one
D)p or q, or not-p or not-q
E)p or q, but p is more likely than q

Question 9

A disjunctive syllogism is a deductive argument with a disjunctive premise, a premise _____ one of the disjuncts, and a conclusion _____ the remaining disjunct(s).

A)negating; affirming
B)affirming; negating
C)affirming; affirming
D)negating; negating
E)either affirming or negating; either affirming or negating

Question 10

Is it possible to assert two propositions in the same sentence?

A)Yes, because every proposition in a sentence is asserted.
B)Yes, a sentence may assert many propositions.
C)Yes, but a sentence can never assert more than two propositions.
D)No, because whenever there are two propositions in a sentence, only one is asserted.
E)No, because whenever there are two propositions in a sentence, neither is asserted.

Question 11

Suppose that p is the proposition "All whales are mammals." What is the proposition not-p?

A)No whale is a mammal.
B)Some whales are mammals.
C)All mammals are whales.
D)Some mammals are not whales.
E)Some whales are not mammals.

Question 12

If a sentence expresses a compound proposition, is that proposition, taken as a whole, asserted?

A)No, because the component propositions are not asserted.
B)No, because only simple propositions, and not compound ones, can be asserted.
C)No, because a whole sentence can never be asserted.
D)Yes, because every declarative sentence, taken as a whole, is asserted.
E)Yes, because every proposition that is expressed is also asserted.

Question 13

Suppose that p is the proposition "Some subatomic particles are not leptons." What is the proposition not-p?

A)Some leptons are not subatomic particles.
B)Some subatomic particles are leptons.
C)All subatomic particles are leptons.
D)No subatomic particle is a lepton.
E)No lepton is a subatomic particle.

Question 14

Suppose that p is the proposition "Some mushrooms are hallucinogens." What is the proposition not-p?

A)Some mushrooms are not hallucinogens.
B)All mushrooms are hallucinogens.
C)No mushroom is a hallucinogen.
D)All hallucinogens are mushrooms.
E)Some hallucinogens are mushrooms.

Question 15

Which of the following is a compound proposition?

A)Whales are mammals.
B)Whales are very large fish.
C)No whale is a reptile.
D)Some whales are reptiles.
E)Whales are mammals or whales are very large fish.

Question 16

Suppose that the first premise of a syllogism is a disjunctive proposition, and the second premise affirms one of the disjuncts.Is the syllogism valid?

A)No, because the second premise must negate a disjunct rather than affirm it.
B)No, because the disjunctive premise ought to be second rather than first.
C)Yes, if the conclusion affirms the remaining disjunct(s).
D)Yes, if the conclusion negates the remaining disjunct(s).
E)Yes, if the conclusion either affirms or negates the remaining disjunct(s).

Question 17

In disjunctive or hypothetical propositions, the component propositions are:

A)asserted, but not expressed
B)expressed, but not asserted
C)both asserted and expressed
D)neither asserted nor expressed
E)sometimes asserted, sometimes expressed, but never both

Question 18

Could there exist a proposition, p, for which there is no corresponding proposition, not-p?

A)Yes, because I and O propositions do not have contraries.
B)Yes, because some propositions are already negative and cannot be negated again.
C)Yes, because some propositions are inherently affirmative and therefore cannot be negated.
D)No, because every proposition has a contrary.
E)No, because every proposition can be contradicted.

Question 19

Suppose that p is the proposition "It is raining." What is the proposition not-p?

A)It is not raining.
B)It may or may not be raining.
C)It will continue to rain.
D)The rain will stop soon.
E)It was raining.

Question 20

Which of the following is a compound proposition?

A)If the baby wakes, I will pick her up.
B)Nothing in the world is as sad as a crying clown.
C)For every worker, there was a first earned dollar.
D)Growing an investment takes time.
E)My dream is to swim with a pod of dolphins.

Question 21

Suppose that one premise of a disjunctive syllogism is "There are some millionaires in our town" and the conclusion is "The Smiths are millionaires." What is the unstated premise?

A)There are no millionaires in our town, or the Smiths are millionaires.
B)If the Smiths are millionaires, then there are some millionaires in our town.
C)The Smiths live in our town.
D)The Smiths are the only millionaires in our town.
E)It is clear who the millionaires in our town are.

Question 22

Can the disjunctive premise of a disjunctive syllogism contain more than two disjuncts?

A)Only if the syllogism is part of a larger argument that includes additional syllogisms.
B)Yes, but not more than three.
C)Yes, but not more than four.
D)Yes.
E)No.

Question 23

Is the following syllogism valid? Either all tigers are good dancers, or no tiger wedding is fun.
No tiger is a good dancer.
No tiger wedding is fun.

A)Yes.
B)No, because the conclusion is negative.
C)No, because the disjunctive premise is not in standard form.
D)No, because the disjunctive premise is false.
E)It depends on your view of existential import.

Question 24

What conclusion follows from these premises? The vaccine was ineffective or unavail able, or the patient did not wish to receive it. The vaccine was avail able.

A)The vaccine was ineffective or the patient did not wish to receive it.
B)The vaccine was ineffective.
C)The patient did not wish to receive the vaccine.
D)The patient wished to receive the vaccine.
E)The vaccine was effective.

Question 25

Is the following syllogism valid? Either there is an accounting error, or some of our members are not paying their dues.
All of our members are paying their dues.
There is an accounting error.

A)Yes.
B)No, because the disjunctive premise is not in standard form.
C)No, because the second premise does not deny any of the disjuncts.
D)No, because even if the premises are true, the conclusion could be false.
E)It depends on your view of existential import.

Question 26

Can a coherent argument assert a disjunctive proposition, and then deny all of its disjuncts?

A)Yes, if each of the disjuncts could be denied, then they could all be denied.
B)Yes, because a disjunctive proposition does not assert that its disjuncts are true.
C)Yes, because the conclusion might be some combination of the disjuncts, rather than any particular one of them.
D)No, because whenever there is a disjunctive premise, there must be another premise that affirms at least one of the disjuncts.
E)No, because the disjunctive proposition asserts that at least one of the disjuncts is true.

Question 27

If we began a murder investigation with five suspects, how many disjunctive syllogisms would be required to determine the culprit?

A)one
B)two
C)three
D)four
E)five

Question 28

Suppose that one premise of a disjunctive syllogism is "Some forts are not well protected or these knights are amazingly good at capturing forts" and the conclusion is "These knights are amazingly good at capturing forts." What is the unstated premise?

A)Some forts are well protected.
B)All forts are well protected.
C)These knights capture forts.
D)These knights have captured some forts.
E)Poorly protected forts are easier to capture.

Question 29

Is the following syllogism valid? Either some of this food contains peanuts, or I am reacting to a different allergen.
Some of this food does not contain peanuts.
I am reacting to a different allergen.

A)Yes.
B)No, because the "different allergen" is never identified.
C)No, because the disjunctive premise is not in standard form.
D)No, because the second premise does not deny any of the disjuncts.
E)It depends on your view of existential import.

Question 30

What conclusion follows from these premises? Someone will cook supper or no one will eat.
Someone will eat.

A)Something will be eaten.
B)Something will be cooked.
C)No one will cook supper.
D)Someone will not eat.
E)Someone will cook supper.

Question 31

Suppose that the first premise of a disjunctive syllogism is the disjunctive proposition.Must the second proposition be affirmative or negative?

A)Affirmative, because it must affirm one of the disjuncts.
B)Affirmative, because if it were negative, it wouldn't really tell us anything.
C)It can be either one, as long as it negates a disjunct.
D)It can be either one, as long as it has the opposite of the quality of the conclusion.
E)Negative, because it must negate one of the disjuncts.

Question 32

Is the following syllogism valid? Tom is asleep or Tom is reading.
Tom is asleep.
Tom is not reading.

A)Yes.
B)No, because the conclusion is a negative proposition.
C)No, because the disjunctive premise ought to be the second premise, not the first.
D)No, because we don't know whether or not the second premise is true.
E)No, because the second premise affirms a disjunct rather than negating one.

Question 33

What conclusion follows from these premises? The camp does not offer both swimming and boating.
The camp offers swimming.

A)The camp has a lake.
B)The camp is concerned about the safety of swimmers around boats.
C)The camp does not offer boating.
D)The camp's lake is too small for boating.
E)The camp offers boating.

Question 34

What conclusion follows from these premises? The meeting is in room 305 or the meeting is in room 306 . The meeting is not in room 305 .

A)The meeting is not in room 306.
B)The meeting is in room 306.
C)The meeting has been moved.
D)The meeting might be canceled.
E)The meeting will definitely happen.

Question 35

Suppose that one premise of a disjunctive syllogism is "My book is not in my bag" and the conclusion is "I left my book at the library." What is the unstated premise?

A)My book is in my bag.
B)I didn't leave my book at the library.
C)My book is in my bag or I left my book at the library.
D)My book is not in my bag or I didn't leave my book at the library.
E)If I left my book at the library, then my book is not in my bag.

Question 36

Is the following syllogism valid? The child is not a girl or the child is not a boy.
The child is a girl.
The child is not a boy.

A)Yes.
B)No, because the conclusion is a negative proposition.
C)No, because the disjunctive premise ought to be the second premise, not the first.
D)No, because we don't know whether or not the second premise is true.
E)No, because the second premise affirms a disjunct rather than negating one.

Question 37

Suppose that the first premise of a disjunctive syllogism is "p or q." What must the second premise be?

A)p
B)q
C)not-p
D)it could be not-p, or it could be not-q
E)not-q

Question 38

The components of a disjunctive proposition are called:

A)syllogisms
B)terms
C)disjuncts
D)concepts
E)semiprops

Question 39

Suppose that one premise of a disjunctive syllogism is "Rachael or Susan will be Jenna's maid of honor" and the conclusion is "Susan will be Jenna's maid of honor." What is the unstated premise?

A)Jenna likes Susan more than she likes Rachael.
B)Jenna is getting married.
C)Rachael will not be Jenna's maid of honor.
D)Jenna doesn't like Rachael.
E)Jenna can only choose one maid of honor.

Question 40

Is the following argument valid? At the party, there will be sodas, bottled water, beer, or wine.
There will be no wine at the party.
There will be sodas and bottled water at the party.
There will be no beer at the party.

A)Yes.
B)No, because the third premise affirms disjuncts rather than negating them.
C)No, because the second premise affirms a disjunct rather than negating one.
D)No, because there are too many premises.
E)No, because the conclusion is a negative proposition.

Question 41

Which disjunctive proposition is logically equivalent to the following categorical proposition? No S is P.

A)A thing is not S, or it is P.
B)A thing is S, or it is P.
C)A thing is not S, or it is not P.
D)A thing is S, or it is not P.
E)No disjunctive proposition is equivalent.

Question 42

Does every disjunctive proposition have an equivalent hypothetical proposition, such that the hypothetical could replace the disjunctive in any argument without otherwise changing the argument's structure?

A)Yes, since replacing a proposition with another that is logically equivalent never has any effect on the structure of the argument.
B)Yes, since if one disjunctive proposition has such an equivalent, they all must.
C)No, since replacing one proposition with another will always have a significant effect on the structure of an argument.
D)No, since some disjunctive propositions contain more than two disjuncts.
E)No, since no disjunctive proposition ever has an equivalent hypothetical proposition.

Question 43

What is the contrapositive of the proposition "If it rained last night, then the ground is wet this morning"?

A)If it didn't rain last night, then the ground is wet this morning.
B)If it rained last night, then the ground isn't wet this morning.
C)If it didn't rain last night, then the ground isn't wet this morning.
D)If the ground is wet this morning, then it rained last night.
E)If the ground isn't wet this morning, then it didn't rain last night.

Question 44

The "if" part of a hypothetical proposition is called the:

A)antecedent
B)consequent
C)disjunct
D)genus
E)species

Question 45

In a true hypothetical proposition:

A)the truth of the antecedent is sufficient to guarantee the truth of the consequent
B)the truth of the consequent is sufficient to guarantee the truth of the antecedent
C)the antecedent could be true, while the consequent is false
D)the truth of the antecedent tells us nothing about the truth of the consequent
E)the antecedent and consequent cannot both be false

Question 46

Can an argument have more than one disjunctive premise?

A)Yes, because sometimes more than one disjunctive proposition is required to express a large number of possibilities.
B)Yes, there is no limit to the number of disjunctive premises.
C)Yes, because there must be one disjunctive premise for every categorical premise.
D)No, because that would require the argument to have two different conclusions.
E)No, because only one disjunct can be true, so every disjunctive premise after the first would consist entirely of false disjuncts.

Question 47

Hypothetical propositions are most like which type of categorical proposition?

A)A
B)E
C)I
D)O
E)U

Question 48

The "then" part of a hypothetical proposition is called the:

A)antecedent
B)consequent
C)disjunct
D)genus
E)species

Question 49

What is the converse of the proposition "If I am energetic, then I will jog"?

A)If I am not energetic, then I will jog.
B)If I am energetic, then I will not jog.
C)If I am not energetic, then I will not jog.
D)If I jog, then I am energetic.
E)If I don't jog, then I am not energetic.

Question 50

Which disjunctive proposition is logically equivalent to the following categorical proposition? All S are P.

A)A thing is not S, or it is P.
B)A thing is S, or it is P.
C)A thing is not S, or it is not P.
D)A thing is S, or it is not P.
E)No disjunctive proposition is equivalent.

Question 51

What is the consequent of the proposition "If it rains, then the graduation will be held in the gym"?

A)graduation
B)gym
C)the graduation will be held in the gym
D)it rains
E)if

Question 52

If the disjunctive premise of a disjunctive argument is "p or (not-p or q)," then:

A)the conclusion cannot be p
B)the conclusion cannot be not-p
C)the conclusion cannot be q
D)the conclusion must be q
E)the conclusion must be not-p

Question 53

What is the antecedent of the proposition "If it rains, then the graduation will be held in the gym"?

A)graduation
B)gym
C)the graduation will be held in the gym
D)it rains
E)if

Question 54

If an argument contains a disjunctive premise, must the conclusion appear as one of the disjuncts in that premise?

A)Yes, because an argument with a disjunctive premise simply consists of denying disjuncts until only one is left.
B)Yes, because otherwise the disjunctive premise would play no role in the argument.
C)Yes, because the conclusion of a deductive argument is always entailed by the premises.
D)No, because the disjunctive part of the argument might only be one step on the way to the conclusion.
E)No, because the conclusion must be the denial of one of the disjuncts.

Question 55

Which hypothetical proposition is logically equivalent to the following disjunctive proposition? p or q

A)if p, then q
B)if p, then not q
C)if not p, then q
D)if not p, then not q
E)if and only if p, then q

Question 56

The form of a hypothetical proposition is:

A)p or q
B)p and q
C)p but not q
D)q but not p
E)if p, then q

Question 57

If the disjunctive premise of a disjunctive argument has N disjuncts, and the conclusion is one of those disjuncts, then how many syllogisms make up the argument?

A)N
B)2N
C)N +1
D)N F-1
E)N/2

Question 58

Is a hypothetical proposition equivalent to its converse? To its contrapositive?

A)It is equivalent to its converse, but not to its contrapositive.
B)It is equivalent to its contrapositive, but not to its converse.
C)It is equivalent to both.
D)It is equivalent to neither.
E)It depends on the subject matter of the proposition.

Question 59

When is a disjunctive proposition false?

A)when its disjuncts bear no relation to each other at all
B)when two or more of its disjuncts are both true
C)when one of its disjuncts is false
D)when all of its disjuncts are false
E)A disjunctive proposition is never false, since it is not asserted.

Question 60

Suppose that the first premise of a disjunctive syllogism is the disjunctive premise.Could the second premise ever be affirmative, without committing the fallacy of affirming a disjunct?

A)No, because it is only permissible to deny one of the disjuncts, and an affirmative proposition cannot do that.
B)No, because no affirmative proposition has a distributed predicate term.
C)Yes, but only if every disjunct is negative.
D)Yes, because one of the disjuncts could be affirmative.
E)Yes, because one of the disjuncts could be negative.

Question 61

What would the following proposition be in standard form? p if and only if q

A)if p, then q and if q, then p
B)if p, then q
C)if q, then p
D)if not p, then q
E)if not q, then p

Question 62

Generally, "without X, q" can be translated into standard form as:

A)if X does not exist (or occur), then q
B)if X exists (or occurs), then q
C)if q, then X exists (or occurs)
D)if q, then X does not exist (or occur)
E)if not q, then X does not exist (or occur)

Question 63

What is the contrapositive of the proposition "Without credibility, threats are useless"?

A)If they have credibility, threats are useful.
B)If they have credibility, threats are useless.
C)If they have no credibility, threats are useful.
D)If threats are useful, then they have credibility.
E)If threats are useless, then they have credibility.

Question 64

Is it acceptable for the antecedent and the consequent to be different types of proposition (categorical, hypothetical, or disjunctive)?

A)Yes, any combination of types is acceptable.
B)No, since they must both be categorical.
C)No.They can be any type of proposition, but they must be the same.
D)Mixing of disjunctives and categoricals is okay.(But hypotheticals are not allowed.)
E)Mixing of hypotheticals and categoricals is okay.(But disjunctives are not allowed.)

Question 65

What is the consequent of the proposition "This stain will not come out unless it is treated immediately"?

A)The stain will not come out.
B)The stain will come out.
C)There is a stain.
D)The stain is treated immediately.
E)The stain is not treated immediately.

Question 66

Suppose that we open a randomly chosen book and examine its first and last sentences.We label the first sentence as p and use it as the premise of a syllogism.And we label the last sentence as q and use it as the conclusion of that same syllogism.Is it always possible to create a valid syllogism by adding "If p, then q" as a second premise?

A)Yes, but the hypothetical premise might strain credibility.
B)Yes, but only because they come from the same book.
C)No, because p and q might be completely unrelated.
D)No, because the resulting syllogism would be invalid.
E)No, because if that worked, you could use any proposition to argue for any other proposition.

Question 67

What would the following proposition be in standard form? Without distribution requirements, most students would take too narrow a range of courses.

A)If most students take too narrow a range of courses, then distribution requirements do not exist.
B)If distribution requirements did not exist, then most students would take too narrow a range of courses.
C)If distribution requirements did not exist, then most students would not take too narrow a range of courses.
D)If distribution requirements exist, then most students will not take too narrow a range of courses.
E)If distribution requirements exist, then most students will take too narrow a range of courses.

Question 68

Which disjunctive proposition is equivalent to this hypothetical proposition? If and only if p, then q.

A)p or q
B)p or not q
C)not p or not q
D)not p or q
E)( p or not q) and (not p or q)

Question 69

Must the antecedent and the consequent of a hypothetical proposition be affirmative?

A)Only the antecedent must be affirmative.
B)Only the consequent must be affirmative.
C)Both must be affirmative.
D)It doesn't matter whether either of them is affirmative or negative.
E)They can both be affirmative or both be negative, but it is not allowed for one to be affirmative while the other is negative.

Question 70

Which categorical proposition is logically equivalent to this hypothetical proposition? If p, then not q.

A)Some cases in which q is true are cases in which p is true.
B)All cases in which p is true are cases in which q is true.
C)No case in which p is true is a case in which q is true.
D)All cases in which q is true are cases in which p is true.
E)Some cases in which p is true are cases in which q is not true.

Question 71

What is the antecedent of the proposition "This stain will not come out unless it is treated immediately"?

A)The stain will not come out.
B)The stain will come out.
C)There is a stain.
D)The stain is treated immediately.
E)The stain is not treated immediately.

Question 72

When is a hypothetical proposition false?

A)A hypothetical proposition cannot be false because it is not asserted.
B)When its antecedent is false.
C)When its consequent is false.
D)When its antecedent and consequent are both false.
E)When its antecedent is true and its consequent is false.

Question 73

When a proposition is put into standard form, the order of its elements will be:

A)if, consequent, then, antecedent
B)if, antecedent, then, consequent
C)if, then, consequent, antecedent
D)consequent, if, then, antecedent
E)antecedent, if, then, consequent

Question 74

What would the following proposition be in standard form? p only if q

A)if not p, then not q
B)if not p, then q
C)if p, then q
D)if q, then p
E)if not q, then p

Question 75

What would the following proposition be in standard form? p unless q

A)if p, then q and if q, then p
B)if p, then q
C)if q, then p
D)if q, then not p
E)if not q, then p

Question 76

Which disjunctive proposition is equivalent to this hypothetical proposition? If p, then q.

A)p or q
B)p or not q
C)not p or not q
D)not p or q
E)(p or not q) and (not p or q)

Question 77

What would the following proposition be in standard form? p if q

A)if q, then p
B)if p, then q
C)if not p, then q
D)if q, then not p
E)if not q, then not p

Question 78

What is the converse of the proposition "I will enjoy the movie only if it is funny"?

A)If the movie is funny, then I will not enjoy it.
B)If the movie is funny, then I will enjoy it.
C)If I enjoy the movie, then it is funny.
D)If I do not enjoy the movie, then it is funny.
E)If I do not enjoy the movie, then it is not funny.

Question 79

Does every hypothetical proposition have an equivalent disjunctive proposition, such that the disjunctive could replace the hypothetical in any argument without otherwise changing the argument's structure?

A)Yes.
B)No, since replacing one proposition with another will always have a significant effect on the structure of an argument.
C)No, since no hypothetical proposition has an equivalent disjunctive proposition.
D)No, since some disjunctive propositions contain more than two disjuncts.
E)No, since certain propositions can be hypothetical antecedents, but can never be disjuncts.

Question 80

Which categorical proposition is equivalent to this hypothetical proposition? If p, then q.

A)Some cases in which q is true are cases in which p is true.
B)All cases in which p is true are cases in which q is true.
C)No case in which p is true is a case in which q is true.
D)All cases in which q is true are cases in which p is true.
E)Some cases in which p is true are cases in which q is not true.