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 conclusions logically follow the given statements.
Statements:
I. All R is M.
II. Some S is R.
Conclusions:
I. Some R is S.
II. Some M is not R.
III. Some R is M.
Option 1: Only conclusion II follows
Option 2: Both conclusions I and III follow
Option 3: All conclusions follow
Option 4: Both conclusions I and II follow
Correct Answer: Both conclusions I and III follow
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions –
Conclusion I:
Some R is S – From the Venn diagram, it is evident that the circles representing R and S overlap and have some parts of their area in common. So, from this, it can be concluded that some R is S. Thus, this conclusion follows.
Conclusion II:
Some M is not R – It is a possibility that the circle representing M is not completely overlapped by the circle representing R. But this is not definite. Thus, this conclusion does not follow.
Conclusion III:
Some R is M – From the Venn diagram, it is evident that the circle representing R is completely overlapped by the circle representing M. Since all R is M, some R will definitely be M. Thus, this conclusion follows.
So, both conclusions I and III follow. Hence, the second option is correct.
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