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:
Some P is K.
No K is T.
Conclusions:
I. All P is T.
II. All T is K.
III. Some P is not T.
Option 1: Only conclusion II follows
Option 2: Only conclusion III follows
Option 3: All conclusions follow
Option 4: Both conclusions II and III follow
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Correct Answer: Only conclusion III follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All P is T – From the Venn diagram, it is evident that there is no direct relation between P and T. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (II):
All T are K – From the Venn diagram, it is evident that there is a negative relation between T and K. So, this conclusion does not follow.
Conclusion (III):
Some P are not T – From the Venn diagram, it is evident that the circles representing P and K overlap and have a part of their area in common. So, it can be concluded that some P that are K are not T.
So, the only conclusion III follows. Hence, the second option is correct.
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