GATE ECE 2021 | GA Question: 6

Question

Given below are two statements and two conclusions.

• $\text{Statement 1}$: All purple are green.
• $\text{Statement 2}$: All black are green.

• $\text{Conclusion I}$: Some black are purple.
• $\text{Conclusion II}$: No black is purple.

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

• A. Only conclusion $\text{I}$ is correct
• B. Only conclusion $\text{II}$ is correct
• C. Either conclusion $\text{I}$ or $\text{II}$ is correct
• D. Both conclusion $\text{I}$ and $\text{II}$ are correct

Answer 1

Given statements are: 

• $\text{Statement 1}$: All purple are green.

• $\text{Statement 2}$: All black are green.

A conclusion “should always be true”. We can try to make the complement of the conclusion satisfiable (by drawing a Venn diagram) and if we can’t then the conclusion is VALID or else NOT Valid.

For the first conclusion “Some black are purple” – the complement is “No black is purple”. It is possible as shown below. So the given conclusion is NOT valid.

For the second conclusion “No black is purple” – the complement is “Some black is purple”. It is possible as shown below. So the given conclusion is NOT valid.

So, options A, B, and D are false. Option C is correct because we cannot make a Venn diagram making both the conclusions false. If we make conclusion $1$ false, the Venn diagram will satisfy conclusion $2$ and vice versa.

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