Question 1

All conservatives favor small government. Colleen favors small government. Therefore, Collen is a conservative. This syllogism is:

Accepted Answer

The middle term, "small government," is not distributed in either premise.

Question 2

In formal logic, an argument in which the conclusion necessarily follows from the premises, if the premises are true, refers to:

Accepted Answer

A syllogism is a type of deductive argument in which the conclusion necessarily follows from the premises, if the premises are true. Therefore, B is the correct choice. An enthymeme is an argument with an implied premise or conclusion. The Toulmin model is a model of argumentation that includes an assertion, evidence, and a warrant. An inductive argument is an argument in which the conclusion is probable, rather than necessarily following from the premises.

Question 3

Soundness refers to a syllogism in which:

Accepted Answer

Soundness refers to a syllogism in which the premises are true, and the conclusion is valid.

Question 4

The three basic types or forms of the syllogism are:

Accepted Answer

The three basic types or forms of the syllogism are categorical, conditional, and disjunctive. Universal, conditional, nonconditional are not the correct categorization of syllogisms. Valid, invalid, and unsound refer to the quality of the syllogism rather than the form. True, false, and uncertain are not relevant to the categorization of syllogisms.

Question 5

All guys who like bowling enjoy beer. Chuck is a guy who likes bowling. Therefore, Chuck enjoys beer. This syllogism is:

Accepted Answer

This syllogism is valid because it follows the correct form of modus ponens, which states that if A implies B and A is true, then B must be true. In this case, the premise “All guys who like bowling enjoy beer” implies that if someone likes bowling (A), they enjoy beer (B). Since Chuck is a guy who likes bowling (A), we can conclude that he enjoys beer (B).

Question 6

All squares have four sides. Some rectangles have four sides. Therefore, some squares are rectangles. This syllogism is:

Accepted Answer

The syllogism is invalid because it commits the fallacy of the undistributed middle term. The fact that both squares and some rectangles have four sides does not logically lead to the conclusion that some squares are rectangles.

Question 7

A categorical syllogism has:

Accepted Answer

A categorical syllogism has three terms: a major term, a minor term, and a middle term, which serves to connect the premises leading to a conclusion.

Question 8

All men are human beings. All women are human beings. Therefore, all men are women. This syllogism is:

Accepted Answer

The syllogism is invalid due to an undistributed middle term. The middle term "human beings" is not distributed in either the major or minor premise, leading to a logical fallacy where the conclusion does not logically follow from the premises.

Question 9

A restaurant owner makes the following deductive argument: "If our food is too spicy, then customers would complain. Customers have complained. Therefore, our food is too spicy." The owner's argument is most accurately described as:

Accepted Answer

The argument is an example of affirming the consequent, which is a logical fallacy. It assumes that because the consequence (customers complaining) occurred, the cause must be the specific one mentioned (food being too spicy), ignoring other possible reasons for complaints.

Question 10

A restaurant owner makes the following deductive argument: "If our food is too spicy, then customers would complain. Customers have not complained. Therefore, our food is not too spicy." This syllogism is:

Accepted Answer

The argument is a valid form of logical reasoning known as "denying the consequent." It follows the structure: If P, then Q. Not Q, therefore not P. In this case, P is "our food is too spicy," and Q is "customers would complain." Since it's stated that customers have not complained (Not Q), the conclusion is that the food is not too spicy (Not P).

Question 11

Some A are B.All C are D. Therefore, some A are D. This syllogism is:

Accepted Answer

The answer of Some A are B.All C are D....

Question 12

No horned mammals are carnivores. All rhinos are horned mammals. Therefore, no rhinos are carnivores. This syllogism is:

Accepted Answer

The syllogism is valid because it follows the pattern of "All A are B, and no B are C, therefore no A are C," which is a valid form of deductive reasoning known as the "Euler diagram" or "Euler's circles" method. In this case, "Horned mammals" are the A, "Carnivores" are the C, and "Rhinos" are the B. Therefore, the conclusion that "no rhinos are carnivores" logically follows from the premises.

Question 13

All cyclops are one-eyed. Some trolls are not one-eyed. Therefore, some trolls are not cyclops. This syllogism is:

Accepted Answer

The syllogism is valid as it follows the pattern of the valid syllogism called "I-O". The premise "All cyclops are one-eyed" is an "I" statement, and the premise "Some trolls are not one-eyed" is an "O" statement. When we put these together, we get the conclusion "Some trolls are not cyclops," which is also an "O" statement. Therefore, the syllogism is valid.

Question 14

Jane is either a soccer fan or she is a basketball fan. Jane is not a basketball fan. Therefore, Jane is a soccer fan. This syllogism is:

Accepted Answer

This is a valid deductive argument that follows the logical form of modus tollens. If A implies B, and B is false, then A must be false as well. In this case, "Jane is not a basketball fan" is the false statement, so the only remaining option is that "Jane is a soccer fan."

Question 15

Which statement about the validity and soundness of syllogisms is most accurate?

Accepted Answer

Validity is a necessary condition for soundness. If a conclusion is sound, it must be valid, but a valid conclusion may not necessarily be sound if the premises are false or unsupported. Therefore, option B is the most accurate statement about the validity and soundness of syllogisms.

Question 16

All parrots have feathers. Some pets are parrots. Therefore, some pets have feathers. This syllogism is:

Accepted Answer

The syllogism follows a logical structure where the conclusion (some pets have feathers) directly follows from the premises (all parrots have feathers and some pets are parrots), making it valid.

Question 17

Which of the following accurately describes "soundness" as it relates to syllogisms?

Accepted Answer

Soundness refers to the validity of a syllogism, which means that the conclusion logically follows from the premises. In order for a syllogism to be sound, the premises must be true and the conclusion must be valid (meaning it logically follows from the premises). Therefore, choice D (The premises are true, and the conclusion is valid) accurately describes soundness.

Question 18

Darlene laments, "It's Friday night. Either I stay home and wish I went out, or I go out and wish I stayed home." What type of syllogism has Darlene offered?

Accepted Answer

The answer of Darlene laments, "It's Friday night. Either I...

Question 19

That bird is either a raven or a crow. Ravens have dense, shaggy plumage. That bird has dense, shaggy plumage. Therefore, that bird is a raven. This syllogism is:

Accepted Answer

The answer of That bird is either a raven or...

Question 20

All snakes that are venomous are carnivorous. All snakes that are constrictors are carnivorous. Therefore, all snakes are carnivorous. This syllogism is:

Accepted Answer

The middle term, carnivorous, is not distributed, and it appears in the conclusion. Therefore, the argument is invalid. The fact that all venomous snakes are carnivorous and all constrictor snakes are carnivorous does not necessarily mean that all snakes are carnivorous. There may be some non-venomous and non-constrictor snakes that are not carnivorous.

Quiz 11: Deductive Reasoning