Question : Directions: Two statements are given, followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some colleges are schools.
No ground is a college.
Conclusions:
I. No college is a ground.
II. No school is a college.
III. Some schools are colleges.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I and II follow
Option 3: Only conclusions I and III follow
Option 4: All of the conclusions follow
Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyze the conclusions –
Conclusion (I):
No college is a ground –
From the Venn diagram, it is evident that there is a negative relation between college and ground. Thus, it can be concluded that no college is ground.
Conclusion (II):
No school is a college – From the Venn diagram, it is evident that the circles representing schools and colleges overlap and have some parts of their area in common. Thus, this conclusion does not follow.
Conclusion (III):
Some schools are colleges – From the Venn diagram, it is evident that the circles representing schools and colleges overlap and have some parts of their area in common. Thus, it can be concluded that some schools are colleges.
So, only conclusions I and III follow. Hence, the third option is correct.
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