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 X is S.
II. All J are X
Conclusions:
I. Some S are not X.
II. Some J are not S.
III. Some J are not X.
Option 1: Both conclusions I and III follow
Option 2: Both conclusions I and II follow
Option 3: Neither conclusion follows
Option 4: Only conclusion I follows
Correct Answer: Both conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some S are not X – From the Venn diagram, it is evident that no X is S as a cross sign between them defines the relation of not. Therefore, some S are not X is a true conclusion.
Conclusion (II):
Some J are not S – From the Venn diagram, it is evident that no X is S as a cross sign between them defines the relation of not and the circle of J is completely overlapped by the circle of X. Therefore, some J are not S is a true conclusion.
Conclusion (III):
Some J are not X – From the Venn diagram, it is evident that the circle of J is completely overlapped by the circle of X. Therefore, this conclusion is false.
So, both conclusions I and II follow. Hence, the second option is correct.
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