Question 1

Is the following syllogism valid? No Internet service provider is a small business. Some businesses in our town are small businesses. Some businesses in our town are not Internet service providers.

Accepted Answer

The syllogism is valid in both traditional and modern views of existential import because it logically follows that if no Internet service provider is a small business, and some businesses in our town are small businesses, then some businesses in our town are not Internet service providers.

Question 2

Is the following syllogism valid? Some unpopular things are high quality. All TV shows canceled after one season are unpopular. Some TV shows canceled after one season are high quality.

Accepted Answer

The answer of Is the following syllogism valid? Some unpopular...

Question 3

Using the modern rules of validity, find the unstated premise of the following enthymeme. All classrooms on our campus have chalkboards.
_______________________________________
All rooms in Gustav Hall have chalkboards.

Accepted Answer

The unstated premise needed to logically connect the given statement to the conclusion is that all rooms in Gustav Hall are classrooms on our campus. This premise ensures that the specific characteristic of having chalkboards, which applies to all classrooms on campus, also applies to all rooms in Gustav Hall.

Question 4

If we are solving an enthymeme and one premise is an O proposition, then the other premise:

Accepted Answer

The answer of If we are solving an enthymeme and...

Question 5

Which terms must appear in the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits.
$\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$
No hedge fund is a bank.

Accepted Answer

The answer of Which terms must appear in the unstated...

Question 6

Using the modern rules of validity, find the unstated conclusion of the following enthymeme. No popular song from the 1980 s is a song about tuning forks. Some songs by Billy Idol are popular songs from the $1980 \mathrm {~s}$.

Accepted Answer

The conclusion that logically follows from the premises is that some songs by Billy Idol are not about tuning forks. This is because the premises establish that no popular song from the 1980s is about tuning forks and some of Billy Idol's songs are popular songs from the 1980s, implying that those songs cannot be about tuning forks.

Question 7

If we are solving an enthymeme with a missing conclusion, and one premise is an O proposition, then the conclusion:

Accepted Answer

If one premise is an O proposition (Some S are not P), the missing conclusion can only be an O proposition (otherwise the argument would be invalid). This is because the O proposition allows for the possibility of some S not being P, and the conclusion must also allow for this possibility.

Question 8

Which terms must appear in the unstated premise of the following enthymeme? All chairs are furniture.
$\underline{\quad\quad\quad\quad\quad\quad\quad}$
Some furniture is not comfortable.

Accepted Answer

The answer of Which terms must appear in the unstated...

Question 9

If we are solving an enthymeme and the conclusion is an A proposition, then the premises:

Accepted Answer

The conclusion of an enthymeme is the proposition that is being argued for. If the conclusion is an A proposition, then the premises must be propositions that support the conclusion. An A proposition is a universal affirmative proposition, which means that it asserts that something is true for all members of a class. In order to support an A proposition, the premises must also be universal affirmative propositions. This is because a particular negative proposition (E) or a particular affirmative proposition (I) cannot support a universal affirmative proposition.

Question 10

If we are solving an enthymeme and the conclusion is an I proposition, then according to the modern view of existential import, the premises:

Accepted Answer

In the context of syllogistic logic, when solving an enthymeme with a conclusion that is an I proposition (which asserts partial existence, "Some S are P"), according to the modern view of existential import, the premises must logically support the conclusion's claim of existence. Therefore, one premise typically affirms existence (an A proposition, "All S are P", implies existence in the modern view) and the other premise (an I proposition, "Some S are P") directly supports the conclusion's claim. This combination ensures that the conclusion's existential claim is adequately grounded in the premises.

Question 11

According to the rules of validity, which terms must be distributed in the unstated premise of the following enthymeme? All chairs are furniture.
$\underline{\quad\quad\quad\quad\quad\quad\quad}$
Some furniture is not comfortable.

Accepted Answer

The answer of According to the rules of validity, which...

Question 12

Using the modern rules of validity, find the unstated premise of the following enthymeme. All chairs are furniture.
$\underline{\quad\quad\quad\quad\quad\quad\quad}$
Some furniture is not comfortable.

Accepted Answer

The given enthymeme can be completed by adding the premise "Some chairs are not comfortable," which logically connects the conclusion "Some furniture is not comfortable" with the premise "All chairs are furniture."

Question 13

If we are solving an enthymeme and the conclusion is an A proposition, then the figure of the syllogism must be:

Accepted Answer

In traditional syllogistic logic, an enthymeme is a syllogism with a missing premise or conclusion. If the conclusion is an A proposition (universal affirmative, e.g., "All S are P"), the syllogism must be in Figure 1 to ensure proper distribution of terms and validity of the argument. Figures 2, 3, and 4 arrange the middle term differently, affecting the validity of certain types of propositions as conclusions. There is no Figure 5 in traditional syllogistic figures.

Question 14

If we are solving an enthymeme and the conclusion is an E proposition, then the premises:

Accepted Answer

In a valid syllogism with an E proposition as the conclusion, one premise must be universal (A or E) to ensure the conclusion's universality, and the other must be negative (E or O) to ensure the conclusion's negativity. An A and an E proposition satisfy these conditions.

Question 15

Using the modern rules of validity, find the unstated conclusion of the following enthymeme. Californiais in the United States.
Some sunny places are not in the United States.

Accepted Answer

The answer of Using the modern rules of validity, find...

Question 16

Using the rules of validity, determine the quality and quantity of the unstated premise of the following enthymeme. All banks are institutions with government-insured deposits.
$\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$
No hedge fund is a bank.

Accepted Answer

The unstated premise is "No bank is a hedge fund." This is a universal negative premise.

Question 17

Using the modern rules of validity, find the unstated premise of the following enthymeme. All people good at playing Santa Claus are good at playing leprechauns.
_________________________________________________________
Some people good at playing leprechauns are women.

Accepted Answer

The unstated premise is that some people good at playing leprechauns are women, and since all people good at playing Santa Claus are good at playing leprechauns, it follows that some women are good at playing Santa Claus. Option B correctly reflects this unstated premise.

Question 18

According to the rules of validity, which terms must be distributed in the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits.
$\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$
No hedge fund is a bank.

Accepted Answer

In the given enthymeme, the unstated premise must connect the two given statements logically. For the conclusion "No hedge fund is a bank" to follow from "All banks are institutions with government-insured deposits," the unstated premise must involve both "hedge fund" and "institutions with government-insured deposits." This is because the conclusion involves hedge funds and banks, and the given premise involves banks and institutions with government-insured deposits. To logically connect these, the distribution of terms must include both the hedge fund (to connect to the conclusion) and institutions with government-insured deposits (to connect to the given premise).

Question 19

Using the modern rules of validity, determine the quality and quantity of the unstated premise of the following enthymeme. All chairs are furniture.
$\underline{\quad\quad\quad\quad\quad\quad\quad}$
Some furniture is not comfortable.

Accepted Answer

The unstated premise must be a particular negative to logically connect the given statements. It likely implies that some chairs (which are furniture) are not comfortable, allowing the conclusion to follow from the given premise.

Question 20

Using the rules of validity, find the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits.
$\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$
No hedge fund is a bank.

Accepted Answer

The unstated premise needed to logically connect the given statements is that no hedge fund is an institution with government-insured deposits. This premise, when combined with the statement that all banks are institutions with government-insured deposits, logically leads to the conclusion that no hedge fund is a bank.

Quiz 7: Categorical Syllogisms

Is the following syllogism valid? No Internet service provider is a small business. Some businesses in our town are small businesses. Some businesses in our town are not Internet service providers.

Is the following syllogism valid? Some unpopular things are high quality. All TV shows canceled after one season are unpopular. Some TV shows canceled after one season are high quality.

Using the modern rules of validity, find the unstated premise of the following enthymeme. All classrooms on our campus have chalkboards. _______________________________________ All rooms in Gustav Hall have chalkboards.

If we are solving an enthymeme and one premise is an O proposition, then the other premise:

Which terms must appear in the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits. $\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$ No hedge fund is a bank.

Using the modern rules of validity, find the unstated conclusion of the following enthymeme. No popular song from the 1980 s is a song about tuning forks. Some songs by Billy Idol are popular songs from the $1980 \mathrm {~s}$ .

If we are solving an enthymeme with a missing conclusion, and one premise is an O proposition, then the conclusion:

Which terms must appear in the unstated premise of the following enthymeme? All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

If we are solving an enthymeme and the conclusion is an A proposition, then the premises:

If we are solving an enthymeme and the conclusion is an I proposition, then according to the modern view of existential import, the premises:

According to the rules of validity, which terms must be distributed in the unstated premise of the following enthymeme? All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

Using the modern rules of validity, find the unstated premise of the following enthymeme. All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

If we are solving an enthymeme and the conclusion is an A proposition, then the figure of the syllogism must be:

If we are solving an enthymeme and the conclusion is an E proposition, then the premises:

Using the modern rules of validity, find the unstated conclusion of the following enthymeme. Californiais in the United States. Some sunny places are not in the United States.

Using the modern rules of validity, find the unstated premise of the following enthymeme. All people good at playing Santa Claus are good at playing leprechauns. _________________________________________________________ Some people good at playing leprechauns are women.

Using the modern rules of validity, determine the quality and quantity of the unstated premise of the following enthymeme. All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

Using the rules of validity, find the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits. $\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$ No hedge fund is a bank.

Quiz 7: Categorical Syllogisms

Is the following syllogism valid? No Internet service provider is a small business. Some businesses in our town are small businesses. Some businesses in our town are not Internet service providers.

Is the following syllogism valid? Some unpopular things are high quality. All TV shows canceled after one season are unpopular. Some TV shows canceled after one season are high quality.

Using the modern rules of validity, find the unstated premise of the following enthymeme. All classrooms on our campus have chalkboards. _______________________________________ All rooms in Gustav Hall have chalkboards.

If we are solving an enthymeme and one premise is an O proposition, then the other premise:

Which terms must appear in the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits. ‾\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}​ No hedge fund is a bank.

Using the modern rules of validity, find the unstated conclusion of the following enthymeme. No popular song from the 1980 s is a song about tuning forks. Some songs by Billy Idol are popular songs from the 1980 s1980 \mathrm {~s}1980 s .

If we are solving an enthymeme with a missing conclusion, and one premise is an O proposition, then the conclusion:

Which terms must appear in the unstated premise of the following enthymeme? All chairs are furniture. ‾\underline{\quad\quad\quad\quad\quad\quad\quad}​ Some furniture is not comfortable.

If we are solving an enthymeme and the conclusion is an A proposition, then the premises:

If we are solving an enthymeme and the conclusion is an I proposition, then according to the modern view of existential import, the premises:

According to the rules of validity, which terms must be distributed in the unstated premise of the following enthymeme? All chairs are furniture. ‾\underline{\quad\quad\quad\quad\quad\quad\quad}​ Some furniture is not comfortable.

Using the modern rules of validity, find the unstated premise of the following enthymeme. All chairs are furniture. ‾\underline{\quad\quad\quad\quad\quad\quad\quad}​ Some furniture is not comfortable.

If we are solving an enthymeme and the conclusion is an A proposition, then the figure of the syllogism must be:

If we are solving an enthymeme and the conclusion is an E proposition, then the premises:

Using the modern rules of validity, find the unstated conclusion of the following enthymeme. Californiais in the United States. Some sunny places are not in the United States.

Using the modern rules of validity, find the unstated premise of the following enthymeme. All people good at playing Santa Claus are good at playing leprechauns. _________________________________________________________ Some people good at playing leprechauns are women.

Using the modern rules of validity, determine the quality and quantity of the unstated premise of the following enthymeme. All chairs are furniture. ‾\underline{\quad\quad\quad\quad\quad\quad\quad}​ Some furniture is not comfortable.

Using the rules of validity, find the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits. ‾\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}​ No hedge fund is a bank.

Which terms must appear in the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits. $\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$ No hedge fund is a bank.

Using the modern rules of validity, find the unstated conclusion of the following enthymeme. No popular song from the 1980 s is a song about tuning forks. Some songs by Billy Idol are popular songs from the $1980 \mathrm {~s}$ .

Which terms must appear in the unstated premise of the following enthymeme? All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

According to the rules of validity, which terms must be distributed in the unstated premise of the following enthymeme? All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

Using the modern rules of validity, find the unstated premise of the following enthymeme. All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

Using the modern rules of validity, determine the quality and quantity of the unstated premise of the following enthymeme. All chairs are furniture. $\underline{\quad\quad\quad\quad\quad\quad\quad}$ Some furniture is not comfortable.

Using the rules of validity, find the unstated premise of the following enthymeme? All banks are institutions with government-insured deposits. $\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}$ No hedge fund is a bank.