GATE ME 2014 Set 1 — Question 2
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
Read the statements:All women are entrepreneurs.
Some women are doctors.Which of the following conclusions can be logically inferred from the above statements?
Some women are doctors.Which of the following conclusions can be logically inferred from the above statements?
Correct answer
(D) Some entrepreneurs are doctors
Solution
Let be the set of women, be the set of entrepreneurs, and be the set of doctors.
Statements:
(B) Incorrect: We only know about women doctors; we don't know if all doctors are women.
(C) Incorrect: does not imply .
Statements:
1. (All women are entrepreneurs)
2. (Some women are doctors)
From (1) and (2), since there are some elements in the intersection of and , and all elements of are also in , those specific elements must also be in the intersection of and . Thus, , which means "Some entrepreneurs are doctors".(A) Incorrect: We only know some women are doctors.(B) Incorrect: We only know about women doctors; we don't know if all doctors are women.
(C) Incorrect: does not imply .
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