Question 1

What type of hypothetical syllogism is the following? If the Romans were a great power, then they never lost a battle. But the Romans were not a great power. So the Romans did lose a battle.

Accepted Answer

This argument commits the fallacy of denying the antecedent. It incorrectly assumes that if the antecedent (the Romans being a great power) is not true, then the consequent (they never lost a battle) must also not be true, which is a logical error.

Question 2

What would the following proposition be in standard form? The faucet is still running, assuming that no one turned it off.

Accepted Answer

The proposition states that assuming that no one turned off the faucet, it is still running. This can be written as "If no one turned the faucet off, then it is still running," which corresponds to option E.

Question 3

Modus ponens and modus tollens are the two forms of _____ hypothetical syllogism.

Accepted Answer

Modus ponens and modus tollens are forms of mixed hypothetical syllogism, where one premise is a conditional statement and the other premise affirms or denies the antecedent or consequent.

Question 4

What type of hypothetical syllogism is the following? If talent scouts attended the music festival, then the music festival was a success. The music festival was a success. So talent scouts attended the music festival.

Accepted Answer

This is an example of affirming the consequent, a logical fallacy. The argument incorrectly assumes that because the consequent ("the music festival was a success") is true, the antecedent ("talent scouts attended the music festival") must also be true, which is not a valid form of argumentation.

Question 5

What would the following proposition be in standard form? I'll stay home tomorrow only if I'm sick.

Accepted Answer

The proposition states that the speaker will only stay home if they are sick, so if they do stay home tomorrow, it must be because they are sick. Therefore, the correct standard form is "If I stay home tomorrow, then I'm sick."

Question 6

What type of hypothetical syllogism is the following? if $p$, then $q$ $q$ $p$

Accepted Answer

This is an example of affirming the consequent, a logical fallacy where one assumes that because the consequent is true, the antecedent must also be true, which is not a valid form of argument.

Question 7

In a pure hypothetical syllogism:

Accepted Answer

In a pure hypothetical syllogism, both premises are hypothetical, meaning they are conditional statements with an "if...then" structure. The conclusion is also hypothetical, as it follows the same conditional structure. An example of a pure hypothetical syllogism is:

If it rains, then the ground will be wet. 
If the ground is wet, then there must have been rain. 
Therefore, if there is no rain, then the ground cannot be wet.

Question 8

What would the following proposition be in standard form? I'll stay home tomorrow if I feel sick.

Accepted Answer

This proposition can be translated as "If I feel sick, then I will stay home tomorrow." Therefore, the best choice is E.

Question 9

What type of hypothetical syllogism is the following? if $p$, then $q$ not p not $q$

Accepted Answer

This syllogism is invalid because it commits the fallacy of denying the antecedent. The correct form should be "if $p$, then $q$; not $q$; therefore, not $p$" for modus tollens, or "if $p$, then $q$; $p$; therefore, $q$" for modus ponens. Denying the antecedent (not $p$) does not logically lead to the conclusion (not $q$).

Question 10

What would the following proposition be in standard form? Barring anything unexpected, you will live to be 82 years old.

Accepted Answer

The proposition states that barring anything unexpected, meaning if nothing unexpected happens, then you will live to be 82 years old. This can be expressed as "If nothing unexpected happens, then you will live to be 82 years old," which is option C.

Question 11

What would the following proposition be in standard form? As long as everyone agrees, we'll move the meeting to Thursday.

Accepted Answer

The proposition is a conditional statement with the antecedent "everyone agrees" and the consequent "we'll move the meeting to Thursday." The best choice that reflects this is D, which is in the standard form of a conditional statement.

Question 12

What type of hypothetical syllogism is the following? if $p$, then $q$ if $q$, then $r$ if $p$, then $r$

Accepted Answer

This is a pure hypothetical syllogism because it follows the form: if $p$, then $q$; if $q$, then $r$; therefore, if $p$, then $r$.

Question 13

What type of hypothetical syllogism is the following? If we made aprofit on the new product line, then we will continue it. We made a profit on the new product line. So we will continue the new product line.

Accepted Answer

This is an example of modus ponens, which follows the structure: If P, then Q. P is true, therefore Q is true.

Question 14

What type of hypothetical syllogism is the following? if $p$, then $q$ $ p$ $q$

Accepted Answer

This is an example of modus ponens, which follows the logical form: if $p$, then $q$; $p$ is true; therefore, $q$ is true.

Question 15

What is the missing conclusion in the following hypothetical syllogism? If the dinosaurs are extinct, then we can only study them from their fossils.And if we can only study them from their fossils, then our knowledge of them will always be incomplete.

Accepted Answer

The conclusion E logically follows from the premises given, connecting the initial condition (dinosaurs being extinct) to the final outcome (our knowledge of them being always incomplete) through the chain of reasoning provided.

Question 16

What type of hypothetical syllogism is the following? if $p$, then $q$ not q not $p$

Accepted Answer

This is an example of modus tollens, which follows the logical form: if $p$, then $q$; not $q$; therefore, not $p$.

Question 17

What type of hypothetical syllogism is the following? If this butterfly's wings had not dried properly, then it would not be able to fly. But it is able to fly. So this butterfly's wings dried properly.

Accepted Answer

This is an example of modus tollens, which follows the form: If P, then Q. Not Q. Therefore, not P. In this case, P is "this butterfly's wings had not dried properly," and Q is "it would not be able to fly." The statement "But it is able to fly" negates Q, leading to the conclusion that P is also false, hence the butterfly's wings dried properly.

Question 18

What would the following proposition be in standard form? The plant will die unless you water it.

Accepted Answer

The proposition is a conditional statement with the antecedent "you don't water the plant" and the consequent "the plant will die." The best choice is D, which represents the conditional statement in the proper order.

Question 19

What is the missing premise in the following hypothetical syllogism? If the moon is full tonight, then the werewolves will be out.So if the moon is full tonight, then I will be staying at home.

Accepted Answer

The missing premise is the connection between the werewolves being out and the person staying at home. Choice A establishes this connection by stating that if the werewolves are out, then the person will stay at home.

Question 20

What type of hypothetical syllogism is the following? If a hiring deci si on is made too quickly, we will have a subpar sal es representative. And if we have a subpar sales representative, then our reputation and sales will suffer. So if a hiring deci sion is made too quickly, then our reputation and sales will suffer.

Accepted Answer

This is a pure hypothetical syllogism because it follows the form: If P then Q, If Q then R, Therefore, if P then R. It logically connects the initial condition to the final outcome through a chain of implications without affirming or denying any antecedent or consequent directly.

Quiz 8: Reasoning With Syllogisms

What type of hypothetical syllogism is the following? If the Romans were a great power, then they never lost a battle. But the Romans were not a great power. So the Romans did lose a battle.

What would the following proposition be in standard form? The faucet is still running, assuming that no one turned it off.

Modus ponens and modus tollens are the two forms of _____ hypothetical syllogism.

What type of hypothetical syllogism is the following? If talent scouts attended the music festival, then the music festival was a success. The music festival was a success. So talent scouts attended the music festival.

What would the following proposition be in standard form? I'll stay home tomorrow only if I'm sick.

What type of hypothetical syllogism is the following? if $p$ , then $q$ $q$ $p$

In a pure hypothetical syllogism:

What would the following proposition be in standard form? I'll stay home tomorrow if I feel sick.

What type of hypothetical syllogism is the following? if $p$ , then $q$ not p not $q$

What would the following proposition be in standard form? Barring anything unexpected, you will live to be 82 years old.

What would the following proposition be in standard form? As long as everyone agrees, we'll move the meeting to Thursday.

What type of hypothetical syllogism is the following? if $p$ , then $q$ if $q$ , then $r$ if $p$ , then $r$

What type of hypothetical syllogism is the following? If we made aprofit on the new product line, then we will continue it. We made a profit on the new product line. So we will continue the new product line.

What type of hypothetical syllogism is the following? if $p$ , then $q$ $p$ $q$

What is the missing conclusion in the following hypothetical syllogism? If the dinosaurs are extinct, then we can only study them from their fossils.And if we can only study them from their fossils, then our knowledge of them will always be incomplete.

What type of hypothetical syllogism is the following? if $p$ , then $q$ not q not $p$

What type of hypothetical syllogism is the following? If this butterfly's wings had not dried properly, then it would not be able to fly. But it is able to fly. So this butterfly's wings dried properly.

What would the following proposition be in standard form? The plant will die unless you water it.

What is the missing premise in the following hypothetical syllogism? If the moon is full tonight, then the werewolves will be out.So if the moon is full tonight, then I will be staying at home.

Quiz 8: Reasoning With Syllogisms

What type of hypothetical syllogism is the following? If the Romans were a great power, then they never lost a battle. But the Romans were not a great power. So the Romans did lose a battle.

What would the following proposition be in standard form? The faucet is still running, assuming that no one turned it off.

Modus ponens and modus tollens are the two forms of _____ hypothetical syllogism.

What type of hypothetical syllogism is the following? If talent scouts attended the music festival, then the music festival was a success. The music festival was a success. So talent scouts attended the music festival.

What would the following proposition be in standard form? I'll stay home tomorrow only if I'm sick.

What type of hypothetical syllogism is the following? if ppp , then qqq qqq ppp

In a pure hypothetical syllogism:

What would the following proposition be in standard form? I'll stay home tomorrow if I feel sick.

What type of hypothetical syllogism is the following? if ppp , then qqq not p not qqq

What would the following proposition be in standard form? Barring anything unexpected, you will live to be 82 years old.

What would the following proposition be in standard form? As long as everyone agrees, we'll move the meeting to Thursday.

What type of hypothetical syllogism is the following? if ppp , then qqq if qqq , then rrr if ppp , then rrr

What type of hypothetical syllogism is the following? If we made aprofit on the new product line, then we will continue it. We made a profit on the new product line. So we will continue the new product line.

What type of hypothetical syllogism is the following? if ppp , then qqq p pp qqq

What is the missing conclusion in the following hypothetical syllogism? If the dinosaurs are extinct, then we can only study them from their fossils.And if we can only study them from their fossils, then our knowledge of them will always be incomplete.

What type of hypothetical syllogism is the following? if ppp , then qqq not q not ppp

What type of hypothetical syllogism is the following? If this butterfly's wings had not dried properly, then it would not be able to fly. But it is able to fly. So this butterfly's wings dried properly.

What would the following proposition be in standard form? The plant will die unless you water it.

What is the missing premise in the following hypothetical syllogism? If the moon is full tonight, then the werewolves will be out.So if the moon is full tonight, then I will be staying at home.

What type of hypothetical syllogism is the following? if $p$ , then $q$ $q$ $p$

What type of hypothetical syllogism is the following? if $p$ , then $q$ not p not $q$

What type of hypothetical syllogism is the following? if $p$ , then $q$ if $q$ , then $r$ if $p$ , then $r$

What type of hypothetical syllogism is the following? if $p$ , then $q$ $p$ $q$

What type of hypothetical syllogism is the following? if $p$ , then $q$ not q not $p$