GATE CE 2016 Set 2 — Question 8
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.If the above statements are facts, which of the following can be logically inferred?I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.If the above statements are facts, which of the following can be logically inferred?I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
Correct answer
(B) III only.
Solution
Let be the set of humans, be the set of mammals, be the set of engineers, and be the set of those who build houses.From the given facts:
1.Fact 1: (All humans are mammals).
2.Fact 2: (Some humans are engineers).
3.Fact 3: (All engineers build houses).
Evaluating the inferences:- Inference I: 'All mammals build houses' (). This is not necessarily true because we only know that engineers build houses, and not all mammals are engineers.
- Inference II: 'Engineers are mammals' (). While we know that the intersection of humans and engineers () is a subset of mammals (), we do not have information about engineers who are not humans. Therefore, we cannot logically infer that all engineers are mammals.
- Inference III: 'Some humans are not engineers' (). In the context of syllogistic reasoning in competitive exams like GATE, the statement 'Some humans are engineers' is typically interpreted to imply that there is also a group of humans who are not engineers. Given the options and the official answer key, this is the only valid inference.
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