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 M.
All L is M.
Conclusions:
I. Some M is not R.
II. Some L is R.
III. Some M is L.
Option 1: Both conclusions II and III follow
Option 2: Only conclusion III follows
Option 3: Both conclusions I and III follow
Option 4: Neither conclusion follows
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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:
Some M is not R – From the above diagram, all R is M so there is a possibility that some M is R and some is not R. But, this is not definite. So, this conclusion doesn't follow.
Conclusion II:
Some L is R – From the above diagram, it can be seen that there is no direct relation between R and L. So, no relation can be drawn from it. So, this conclusion doesn't follow.
Conclusion III:
Some M is L – From the Venn diagram, it is evident that some parts of the circles representing M lie outside the circle representing L while some lie inside. So, it can be concluded that some M is R.
Therefore, only conclusion III follows according to the given statements. Hence, the second option is correct.
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