Question : Directions: In the following question below, some statements are followed by some conclusions. Taking the given statements to be true, even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusions logically follows from the given statements.
Statements:
All plates are pens.
Some pens are pencils.
Conclusions:
I. All the plates are pencils.
II. No plate is a pencil.
III. Some pencils are pens.
Option 1: Only I
Option 2: Only II
Option 3: Only III
Option 4: Both I and III
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Correct Answer: Only III
Solution : The Venn diagram is as follows –
Let's analyse the conclusions –
Conclusion (I):
All plates are pencils – From the above Venn diagram, it is evident that there is no direct relation between plates and pencils. So, no definite relation can be drawn between them. Therefore, this conclusion does not follow.
Conclusion (II):
No plate is pencil – From the above Venn diagram, it is evident that there is no direct relation between plates and pencils. So, no definite relation can be drawn between them. Therefore, this conclusion does not follow.
Conclusion (III):
Some pencils are pens – From the above Venn diagram, it is evident that the circles representing pencils and pens overlap each other and have a part of their areas in common. So, this conclusion follows.
So, only conclusion III follows. Hence, the third option is correct.
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