Question : Directions: In the following question, two statements are given followed by three conclusions I, II, and III. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements.
Statements:
All cups are glasses.
Some cups are pens.
Conclusions:
I. Some pens are cups.
II. Some pens are glasses.
III. Some pens are not cups.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and II follow
Option 4: All conclusions follow
Correct Answer: Only conclusions I and II follow
Solution : The possible Venn diagram for the given statement –
Let's analyse the conclusions –
Conclusion (I):
Some pens are cups – From the Venn diagram, we can see that the circles representing pens and cups intersect and have some areas in common. So, some pens are cups is a true conclusion.
Conclusion (II):
Some pens are glasses – From the Venn diagram, we can see that the circles representing pens and glasses intersect and have some areas in common. So, Some pens are glasses is a true conclusion.
Conclusion (III):
Some pens are not cups – From the Venn diagram, there is no negative relation between pens and cups. So, this conclusion does not follow.
So, only conclusions I and II follow. Hence the third option is correct.
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