Question : Directions: Three 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:
I. All books are pencils.
II. Some pencils are pens.
III. All pens are erasers.
Conclusions:
I. Some erasers are pencils.
II. All pens are books.
III. Some erasers are pens.
Option 1: Only conclusions I and II follow
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and III follow
Option 4: All 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 analyse the conclusions –
Conclusion I:
Some erasers are pencils – In the Venn diagram, it is clear that the circles that represent erasers and pencils intersect and have a part of their area in common. So, some erasers are pencils is a true conclusion.
Conclusion II:
All pens are books – In the Venn diagram, it is clear that there is no definite relation between pens and books. Therefore, this conclusion does not follow.
Conclusion III:
Some erasers are pens – From the Venn diagram, it is evident that some parts of the circle representing erasers lie outside the circle representing pens while some lie inside. So, it can be concluded that some erasers are pens.
So, the only conclusions I and III follow. Hence, the third option is correct.
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