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 A is Y.
II. No Z is A.
Conclusions:
I. All Y are A.
II. Some Y is A.
III Some A is Z.
Option 1: Neither conclusion follows
Option 2: All conclusion follows
Option 3: Only conclusion II follows
Option 4: Both conclusions I and III follow
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All Y are A –
From the Venn diagram, it is evident that some parts of the circle representing Y lie inside the circle representing A while some lie outside. Thus, this conclusion does not follow.
Conclusion (II):
Some Y is A –
From the Venn diagram, it is evident that some parts of the circle representing Y lie inside the circle representing A while some lie outside. Thus, it can be concluded that some Y is A.
Conclusion (III):
Some A is Z –
From the Venn diagram, it is evident that there is a negative relation between A and Z. Thus, this conclusion does not follow.
So, the only conclusion II follows. Hence, the third option is correct.
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