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 are seen 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 U are M
II. All M are J.
Conclusions:
I. All J are U.
II. Some U are J.
III. Some M are U.
Option 1: Only conclusion III follows
Option 2: Both conclusions I and III follow
Option 3: Only conclusion II follows
Option 4: Both conclusions II and III follow
Correct Answer: Both conclusions II and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
All J are U – From the Venn diagram, we can see that the two circles representing J and U overlap and have a part of their area in common. So, this conclusion does not follow.
Conclusion (II):
Some U are J – From the Venn diagram, we can see that the two circles representing U and J overlap and have a part of their area in common. So, this conclusion follows.
Conclusion (III):
Some M are U – From the Venn diagram, we can see that the two circles representing M and U overlap and have a part of their area in common. So, this conclusion follows.
So, the only conclusions II and III follow. Hence, the fourth option is correct.
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