Crossover Aptitude Logical Reasoning: Syllogisms Questions and Answers — Questions and Answers
Question 1: Given the following premises, which conclusion creates a valid syllogism? Premise 1: All innovative solutions are disruptive. Premise 2: Some disruptive things are challenging to implement.
- All innovative solutions are challenging to implement.
- Some innovative solutions are challenging to implement.
- No innovative solutions are challenging to implement.
- No valid conclusion can be drawn. (Correct answer)
Correct answer: No valid conclusion can be drawn.
This syllogism suffers from the fallacy of the undistributed middle term. The middle term, 'disruptive things', is not distributed in either premise, meaning neither premise makes a statement about ALL disruptive things. Premise 1 states all innovative solutions fall into the category of disruptive things, but not that all disruptive things are innovative solutions. Premise 2 only states that SOME disruptive things are challenging. Because the middle term doesn't connect the major and minor terms properly, no logical conclusion can be drawn about the relationship between 'innovative solutions' and 'things that are challenging to implement'.
Question 2: Analyze the following argument: 1. No managers at this company are under 30. 2. All of the data analysts are under 30. Therefore, no data analysts at this company are managers. What is the logical status of this argument?
- Valid (Correct answer)
- Invalid due to two negative premises.
- Invalid due to an undistributed middle term.
- Uncertain
Correct answer: Valid
The argument is a valid categorical syllogism. Let M = Managers, U = People under 30, and D = Data Analysts. The premises are: 1. No M are U. 2. All D are U. The conclusion is: No D are M. This structure is sound because if all data analysts belong to the group of people under 30, and no managers belong to that same group, then the two groups (data analysts and managers) must be mutually exclusive.
Question 3: Which of the following is a fundamental rule for a valid categorical syllogism?
- The syllogism must have at least one negative premise.
- The conclusion can be universal even if both premises are particular.
- The middle term must be distributed in at least one premise. (Correct answer)
- If a term is distributed in the premise, it must be distributed in the conclusion.
Correct answer: The middle term must be distributed in at least one premise.
A core rule for the validity of a categorical syllogism is that the middle term—the term that appears in both premises but not in the conclusion—must be distributed in at least one of the premises. 'Distributed' means the premise makes a claim about every single member of that class. This ensures that the major and minor terms are properly connected. The other options are incorrect statements of syllogistic rules.
Question 4: Consider the following scenario: A project requires a team member who is both a certified programmer and fluent in Spanish. The project lead reasons: 'All our front-end developers are certified programmers. Maria is fluent in Spanish. Therefore, Maria is a perfect fit.' Why is this reasoning flawed?
- It contains a negative premise and an affirmative conclusion.
- The conclusion is valid, but the premises are untrue.
- It commits the fallacy of the undistributed middle.
- It commits the fallacy of four terms. (Correct answer)
Correct answer: It commits the fallacy of four terms.
This argument is flawed because it commits the Fallacy of Four Terms. A valid categorical syllogism must contain exactly three terms. In this case, the terms are: 1) front-end developers, 2) certified programmers, 3) people fluent in Spanish, and 4) Maria. The premises fail to establish a logical link between 'front-end developers' and 'people fluent in Spanish' through a common middle term.
Question 5: Given the premises: 1. Some remote workers are freelancers. 2. All freelancers manage their own taxes. Which conclusion logically follows?
- All remote workers manage their own taxes.
- Some people who manage their own taxes are remote workers. (Correct answer)
- No remote workers manage their own taxes.
- Some freelancers are not remote workers.
Correct answer: Some people who manage their own taxes are remote workers.
This is a valid syllogism. Since 'some remote workers' are part of the 'freelancers' group, and 'all freelancers' are part of the group that 'manage their own taxes', it must follow that at least that same 'some' of remote workers are also in the group that manages their own taxes. Therefore, 'Some people who manage their own taxes are remote workers' is a valid conclusion. The relationship is not necessarily reversible to say 'Some remote workers are people who manage their own taxes,' but the given answer is a direct logical consequence.
Question 6: An argument states: 'If both premises of a syllogism are negative, no valid conclusion can be drawn.' This statement is an example of:
- The Fallacy of the Illicit Major.
- A logical rule known as the Fallacy of Exclusive Premises. (Correct answer)
- The Existential Fallacy.
- A valid form of disjunctive syllogism.
Correct answer: A logical rule known as the Fallacy of Exclusive Premises.
The statement describes a rule of logic called the Fallacy of Exclusive Premises. A valid categorical syllogism cannot have two negative premises. Two negative premises (e.g., 'No A are B' and 'No B are C') fail to establish a connection between the major and minor terms, making it impossible to deduce a relationship.
Crossover Aptitude Logical Reasoning: Syllogisms Questions and Answers
Given the following premises, which conclusion creates a valid syllogism?
Premise 1: All innovative solutions are disruptive.
Premise 2: Some disruptive things are challenging to implement.