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 red are pens. No pen is white. Conclusions: I. No white is a pen. II. No red is white. III. All pens are red.
Option 1: Only I and III
Option 2: Only I and II
Option 3: Only II and III
Option 4: All conclusions follow
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Correct Answer: Only I and II
Solution : The Venn diagram is as follows –
Let's analyse the conclusions – Conclusion (I): No white is a pen – From the given statements, it is evident that no pen is white. So, from this, it can be concluded that no white is a pen. Thus, this conclusion follows. Conclusion (II): No red is white – From the given statements, all red are pens and no pen is white. So, from this, it can be concluded that no red is white. Thus, this conclusion follows. Conclusion (III): All pens are red – From the Venn diagram, it is evident that some part of the circle that represents pens is outside the circle that represents red. So, from this, it can be concluded that some pens are red. Thus, this conclusion does not follow.
So, only conclusions I and II follow. Hence, the second option is correct.
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