GATE EC 2014 Set 1 — Question 2
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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 represent the set of women, represent the set of entrepreneurs, and represent the set of doctors.
Since some women are doctors (), there exists at least one person who is both a woman and a doctor. Because all women are entrepreneurs (), that person (who is a woman and a doctor) must also be an entrepreneur. Therefore, there is at least one person who is both an entrepreneur and a doctor ().This leads to the conclusion: Some entrepreneurs are doctors.
1.Statement 1: All women are entrepreneurs. Mathematically, .
2.Statement 2: Some women are doctors. Mathematically, .
Analysis:Since some women are doctors (), there exists at least one person who is both a woman and a doctor. Because all women are entrepreneurs (), that person (who is a woman and a doctor) must also be an entrepreneur. Therefore, there is at least one person who is both an entrepreneur and a doctor ().This leads to the conclusion: Some entrepreneurs are doctors.
- (A) is incorrect because we only know some women are doctors.
- (B) is incorrect because we only know about the doctors who are women; we have no information about other doctors.
- (C) is incorrect because does not imply .
- (D) is the correct logical inference.
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