Question : Directions: In the following question some statements are given 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 C are D.
II. All D is E.
Conclusions:
I. All C is E.
II. All D is C.
III. All E is D.
Option 1: Only conclusion I follows
Option 2: None of the conclusion follows
Option 3: Only conclusion II follows
Option 4: All conclusion follows
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Correct Answer: None of the conclusion follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All C is E – From the Venn diagram, we can see that the two circles representing E and C intersect and have only a part of their area in common. So, from this, it can be inferred that some E are C. Therefore, this conclusion does not follow.
Conclusion (II):
All D is C – From the Venn diagram, we can see that the two circles representing D and C intersect and have only a part of their area in common. So, from this, it can be inferred that some D are C. Therefore, this conclusion does not follow.
Conclusion (III):
All E is D – From the Venn diagram, we can see that the circle representing D is completely overlapped by the circle representing E. So, all E cannot be D. Therefore, this conclusion does not follow.
So, none of the conclusions follow. Hence the second option is correct.
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