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:
I. Some R is C.
II. All R is K.
Conclusions:
I. All K is R.
II. All C is R.
III. All C is K.
Option 1: Both conclusions II and III follow
Option 2: Both conclusions I and III follow
Option 3: Neither conclusion follows
Option 4: All conclusions follow
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Correct Answer: Neither conclusion follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All K is R – From the Venn diagram, it is evident that some parts of the circle representing K lie outside the circle representing R while some lie inside. So, from this, it can be concluded that some K is R. Thus, this conclusion does not follow.
Conclusion (II):
All C is R – From the Venn diagram, it is evident that the two circles representing C and R overlap and have a part of their areas in common. So, from this, it can be concluded that some C is R. Thus, this conclusion does not follow.
Conclusion (III):
All C is K – From the Venn diagram, it is evident that the two circles representing C and K overlap and have a part of their areas in common. So, from this, it can be concluded that some C is K. Thus, this conclusion does not follow.
So, none of the conclusions follows. Hence, the third option is correct.
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