Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. 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 the given statements.
Statements:
All R is H.
Some T is R.
Conclusions:
I. All H is R.
II. All T is H.
III. No R is T.
Option 1: None of the conclusions follow
Option 2: Both conclusions I and II follow
Option 3: All conclusions follow
Option 4: Only conclusion III follows
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Correct Answer: None of the conclusions follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All H is R – From the Venn diagram, it is evident that some parts of the circle representing H lie inside the circle representing R while some lie outside. So, this conclusion does not follow.
Conclusion (II):
All T is H – From the Venn diagram, it is evident that the two circles representing T and H overlap and have a part of their area in common. So, this conclusion does not follow.
Conclusion (III):
No R is T – From the Venn diagram, it is evident that the two circles representing R and T overlap and have a part of their area in common. So, this conclusion does not follow.
So, none of the conclusions follow. Hence, the first option is correct.
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