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. A. II only. B. III only. C. I and II. D. I only.

GATE 2016 · General Aptitude · Statements Follow · medium

Answer: Only Inference III (Some humans are not engineers) can be logically inferred. Option B is correct.

1. Evaluate Inference I: All mammals build houses: We know some humans (who are mammals) are engineers who build houses. But mammals include non-human animals (dogs, cats, whales) about whom no building claim is made. Inference I is too broad and cannot be established. FALSE.
2. Evaluate Inference II: Engineers are mammals: Fact 2 says 'Some humans are engineers'. This means engineers in question are human. Fact 1 says all humans are mammals. Therefore those engineers are mammals. BUT: the facts say nothing about engineers from non-human sources; however, we can only talk about the given universe. Still, Fact 2 only says SOME humans are engineers — it does not say ALL engineers are humans. Engineers from other species (hypothetically) might exist. Inference II cannot be guaranteed from the facts as stated. FALSE.
3. Evaluate Inference III: Some humans are not engineers: Fact 2 states 'Some humans are engineers', using the word 'some' which in formal logic means 'at least one but not all' (under the standard GATE interpretation of exclusive-some or simply since 'All humans are engineers' is not given). The fact uses 'some', signalling a proper subset relationship. Therefore, there exist humans who are NOT engineers. Inference III is TRUE.