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:
All O is C.
All C is D.
Conclusions:
I. Some C is O.
II. Some D is C.
III. No O is D.
Option 1: Both conclusions II and III follow
Option 2: All conclusions follow
Option 3: Both conclusions I and II follow
Option 4: Both conclusions I and III follow
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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 C is O – From the Venn diagram, it is evident that some parts of the circles representing C lie outside the circle representing O while some lie inside. So, from this, it can be concluded that some C is O. Therefore, this conclusion follows.
Conclusion (II):
Some D is C – From the Venn diagram, it is evident that some parts of the circles representing D lie outside the circle representing C while some lie inside. So, from this, it can be concluded that some D is C. Therefore, this conclusion follows.
Conclusion (III):
No O is D – From the Venn diagram, it is evident that the circle representing O completely lies inside the circle representing D. So, from this, it can be concluded that all O is D. Therefore, this conclusion does not follow.
So, both conclusions I and II follow. Hence, the third option is correct.
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