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. All M are N.
II. Some X are M.
Conclusions:
I. Some X are not N.
II. Some N are not M.
Option 1: Neither conclusion follows
Option 2: Only conclusion I follows
Option 3: Both conclusions I and II follow
Option 4: Only conclusion II follows
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):
Some X are not N –
It is a possibility that the circle representing X is not completely overlapped by the circle representing N. But this is not definite. Thus, this conclusion does not follow.
Conclusion (II):
Some N are not M –
It is a possibility that the circle representing N is not completely overlapped by the circle representing M. But this is not definite. Thus, this conclusion does not follow.
So, neither conclusion follows. Hence, the first option is correct.
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