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:
Some pens are markers.
All markers are crayons.
Conclusions:
I. All pens can never be crayons.
II. At least some crayons are pens.
Option 1: Only conclusion I follows
Option 2: Neither conclusion I nor II follows
Option 3: Both conclusions I and II follow
Option 4: Only conclusion II follows
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions –
Conclusion I:
All pens can never be crayons – It is a possibility that the circle representing pens is completely overlapped by the circle representing crayons. But this is not definite. Thus, this conclusion does not follow.
Conclusion II:
At least some crayons are pens – From the Venn diagram, it is evident that the circles representing pens and crayons overlap and have some parts of their area in common. Thus, it can be concluded that at least some crayons are pens.
So, the only conclusion II follows. Hence, the fourth option is correct.
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