Question : Directions: In the following question, two statements are given followed by two conclusions I and II. 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 pens are pencils.
No pencil is an eraser.
Conclusions:
I. No eraser is a pen.
II. No pen is an eraser.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusions I and II follow
Option 4: Neither conclusion I nor conclusion II follows
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Correct Answer: Both conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
No eraser is a pen – From the Venn diagram and the given statements, it is evident that all the pens are pencils and no pencil is an eraser. So, from this, it can be concluded that no eraser is a pen. Therefore, this conclusion follows.
Conclusion (II):
No pen is an eraser – From the Venn diagram and the given statements, it is evident that all the pens are pencils and no pencil is an eraser. So, from this, it can be concluded that no pen is an eraser. Therefore, this conclusion follows.
So, both conclusions follow. Hence, the third option is correct.
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