GATE Mechanical 2021 Set 2 | GA Question: 6

Question

Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$.

• $\text{Statement 1}:$ All entrepreneurs are wealthy.
• $\text{Statement 2}:$ All wealthy are risk seekers.

• $\text{Conclusion I}:$ All risk seekers are wealthy.
• $\text{Conclusion II}:$ Only some entrepreneurs are risk seekers.

Based on the above statements and conclusions, which one of the following options is $\text{CORRECT}$?

• A. Only conclusion $\text{I}$ is correct
• B. Only conclusion $\text{II}$ is correct
• C. Neither conclusion $\text{I}$ nor $\text{II}$ is correct
• D. Both conclusions $\text{I}$ and $\text{II}$ are correct

Answer 1

Given statements are,

• $\text{Statement 1}:$ All entrepreneurs are wealthy.

• $\text{Statement 2}:$ All wealthy are risk seekers.

• $\text{Conclusion I}:$ All risk seekers are wealthy.

From the above Venn diagram, not all risk seekers are wealthy. So, $\text{conclusion I}$ is false.

• $\text{Conclusion II}:$ Only some entrepreneurs are risk seekers.

From the above Venn diagram, all entrepreneurs are risk seekers. So, $\text{conclusion II}$ is also false.

So, the correct answer is $(C).$

Comments

To prove a conclusion false, one Venn diagram is fine. But to prove a conclusion True you should say no contradicting Venn diagram is possible.

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Yes sir. But in conclusion II, they said only some, and using the $3^{\text{rd}}$ Venn diagram we are able to contradict.