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 boys are human.
II. All humans are hard.
Conclusions:
I. Some hard are not a boy.
II. Some humans are not boys.
III. No hard is human.
Option 1: Both conclusions I and III follow
Option 2: Both conclusions II and III follow
Option 3: Only conclusion I follows
Option 4: Neither conclusion 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 hard are not boy –
It is a possibility that the circle representing hard is not completely overlapped by the circle representing boy. But this is not definite. Thus, this conclusion does not follow.
Conclusion (II):
Some humans are not boys –
It is a possibility that the circle representing humans does not completely overlap with the circle representing boys. But this is not definite. Thus, this conclusion does not follow.
Conclusion (III):
No hard is human –
From the Venn diagram, it is evident that some parts of the circle representing hard lie inside the circle representing human while some lie outside. Thus, this conclusion does not follow.
So, neither conclusion follows. Hence, the fourth option is correct.
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