Basic Ability Logical Deduction and Syllogisms Questions and Answers — Questions and Answers
Question 1: Given the following premises, which conclusion creates a valid syllogism? Premise 1: All novels are books. Premise 2: Some reference materials are not books.
- All novels are reference materials.
- No novels are reference materials.
- Some reference materials are not novels. (Correct answer)
- Some books are not novels.
Correct answer: Some reference materials are not novels.
This is a valid conclusion because it logically follows from the premises. Since all novels are books, and some reference materials are explicitly excluded from the 'books' category, it must be true that those specific reference materials are also not novels. This follows the rule that if a term is distributed in the conclusion, it must be distributed in the premises.
Question 2: A valid categorical syllogism requires three terms: a major term, a minor term, and a middle term. In the syllogism below, what is the middle term? 'All mammals are warm-blooded animals. All whales are mammals. Therefore, all whales are warm-blooded animals.'
- Warm-blooded animals
- Whales
- Mammals (Correct answer)
- Animals
Correct answer: Mammals
The middle term is the one that appears in both premises but not in the conclusion. It serves to link the major and minor terms. In this case, 'mammals' connects 'whales' (minor term) and 'warm-blooded animals' (major term).
Question 3: Which of the following describes a syllogistic fallacy? Statement 1: All dogs are mammals. Statement 2: All cats are mammals.
- Concluding 'Therefore, some mammals are dogs.'
- Concluding 'Therefore, all dogs are cats.' (Correct answer)
- Concluding 'Therefore, no cats are dogs.'
- Concluding 'Therefore, some cats are not mammals.'
Correct answer: Concluding 'Therefore, all dogs are cats.'
This is a syllogistic fallacy known as the 'Fallacy of the Undistributed Middle'. Both 'dogs' and 'cats' are related to 'mammals', but the premises do not establish any direct relationship between dogs and cats. Concluding that all dogs are cats is an invalid deduction.
Question 4: A marketing manager is presented with the following argument: Premise 1: If we increase our social media budget, our website traffic will increase. Premise 2: We increased our social media budget. What is the logically valid conclusion?
- Our website traffic will decrease.
- Our social media budget is now too high.
- Our website traffic will increase. (Correct answer)
- There is no relationship between the budget and traffic.
Correct answer: Our website traffic will increase.
This scenario demonstrates a conditional syllogism, also known as Modus Ponens. The structure is 'If P, then Q. P is true. Therefore, Q must be true.' Since the condition (increasing the budget) was met, the consequence (increased traffic) logically follows.
Question 5: According to the rules of syllogisms, which of the following combinations of premises is not permitted in a valid argument?
- Two universal premises
- One universal and one particular premise
- Two negative premises (Correct answer)
- Two affirmative premises
Correct answer: Two negative premises
A fundamental rule of categorical syllogisms is that no valid conclusion can be drawn from two negative premises. If both premises are negative, they state that two things are separate from a third, which does not establish any connection between the first two things.
Question 6: Analyze the following argument: 1. All professional athletes are in good physical condition. 2. Some musicians are professional athletes. Which of the following conclusions is a logical deduction from the premises?
- All musicians are in good physical condition.
- Some musicians are in good physical condition. (Correct answer)
- No musician is in good physical condition.
- All people in good physical condition are musicians.
Correct answer: Some musicians are in good physical condition.
This is a valid deductive conclusion. Since some musicians fall into the category of 'professional athletes', and all individuals in that category are in good physical condition, it logically follows that at least some musicians must be in good physical condition.
Basic Ability Logical Deduction and Syllogisms Questions and Answers
Given the following premises, which conclusion creates a valid syllogism?
Premise 1: All novels are books.
Premise 2: Some reference materials are not books.