Read the statements: - All women are entrepreneurs. - Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? A. All women are doctors B. All doctors are entrepreneurs C. All entrepreneurs are women D. Some entrepreneurs are doctors

GATE 2014 · General Aptitude · Statements Follow · easy

Answer: D. Some entrepreneurs are doctors

1. Translate premises to set notation: Premise 1: forall x (Woman(x) -> Entrepreneur(x)). Premise 2: exists x (Woman(x) AND Doctor(x)).
2. Apply syllogistic reasoning to derive the conclusion: From Premise 2: exists x such that Woman(x) AND Doctor(x). By Premise 1, this same x satisfies Entrepreneur(x). Therefore: exists x (Entrepreneur(x) AND Doctor(x)), i.e., Some entrepreneurs are doctors.
3. Verify the other options are not valid inferences: A: 'All women are doctors' - not supported (Premise 2 only says SOME). B: 'All doctors are entrepreneurs' - not inferable (doctors outside the women set are unspecified). C: 'All entrepreneurs are women' - this is the converse of Premise 1, which does not follow logically.