Question : Directions: Two statements are given followed by two conclusions numbered I and II. 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:
No pen is paper.
All papers are pencils.
Conclusions:
I. Some pens are pencils.
II. All pencils are pens.
Option 1: Neither conclusion I nor II follows
Option 2: Both conclusions I and II follow
Option 3: Only conclusion I follows
Option 4: Only conclusion II follows
Correct Answer: Neither conclusion I nor II follows
Solution : According to the given statements, the Venn diagram is –
Let us analyse the conclusions one by one –
Conclusion I:
Some pens are pencils – It is a possibility that the circles representing pen and pencils overlap and have a part of their area in common. But this is not definite. Thus, this conclusion does not follow.
Conclusion II:
All pencils are pens – From the Venn diagram, it is evident that all papers are pencils and no paper is pen. Thus, all pencils cannot be paper. So, this conclusion does not follow.
So, neither conclusion I nor II follows. Hence, the first option is correct.
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