Given below are two statements I and II, and two conclusions I and II.
Statement I: All entrepreneurs are wealthy.
Statement II: 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?
A. Only conclusion I is correct
B. Only conclusion II is correct
C. Neither conclusion I nor conclusion II is correct
D. Both conclusions I and II are correct
GATE 2021 · General Aptitude · Statements Follow · medium
Answer: Neither Conclusion I nor Conclusion II follows from the given statements. The correct option is C.
Apply transitive syllogism to the two statements: Statement I: All entrepreneurs are wealthy (E subset W). Statement II: All wealthy are risk seekers (W subset RS). By transitivity: All entrepreneurs are risk seekers (E subset RS). This is the key derived fact.
Test Conclusion I: All risk seekers are wealthy: Conclusion I claims RS subset W (converse of Statement II). The converse of a true statement need not be true. Nothing in the premises tells us that every risk seeker is wealthy. Conclusion I is INCORRECT.
Test Conclusion II: Only some entrepreneurs are risk seekers: Step 1 showed that ALL entrepreneurs are risk seekers (not just some). Saying 'only some' implies there exist entrepreneurs who are NOT risk seekers — this contradicts our derivation. Conclusion II is INCORRECT.