GATE ME 2021 Set 2 — Question 6
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
Given below are two statements 1 and 2, and two conclusions I and II.Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.Based on the above statements and conclusions, which one of the following options is CORRECT?
Statement 2: All wealthy are risk seekers.Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.Based on the above statements and conclusions, which one of the following options is CORRECT?
Correct answer
(C) Neither conclusion I nor II is correct
Solution
Let be the set of entrepreneurs, be the set of wealthy people, and be the set of risk seekers.
Statement 1:
Statement 2:
Combining them: .Conclusion I: 'All risk seekers are wealthy' (). This is not necessarily true as is a subset of , not vice versa.
Conclusion II: 'Only some entrepreneurs are risk seekers'. Since , all entrepreneurs are risk seekers. The phrase 'only some' contradicts 'all'.Therefore, neither conclusion follows.
Statement 1:
Statement 2:
Combining them: .Conclusion I: 'All risk seekers are wealthy' (). This is not necessarily true as is a subset of , not vice versa.
Conclusion II: 'Only some entrepreneurs are risk seekers'. Since , all entrepreneurs are risk seekers. The phrase 'only some' contradicts 'all'.Therefore, neither conclusion follows.
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