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. No rat is a cow.
II. Some animals are rats.
Conclusions:
I. Some animals are cows.
II. Some cows are not rats.
III. All rats are animals.
Option 1: Only conclusion II follows
Option 2: Both conclusions I and II follow
Option 3: Neither conclusion follows
Option 4: Both conclusions I and III follow
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Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions –
Conclusion I:
Some animals are cows – From the Venn diagram, it is evident that there is no direct relation between animals and cows. So, no definite relation can be drawn. Thus, this conclusion does not follow.
Conclusion II:
Some cows are not rats – From the Venn diagram, it is evident that there is a negative relation between cows and rats. Since no cows are rats, so some cows will definitely not be rats. Thus, this conclusion follows.
Conclusion III:
All rats are animals – From the Venn diagram, it is evident that the circles representing rats and animals overlap and have some parts of their area in common. So, from this, it can be concluded that some rats are animals. Thus, this conclusion does not follow.
So, the only conclusion II follows. Hence, the first option is correct.
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