Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
I. Some X are M.
II. Some D are M.
Conclusions:
I. All X are D.
II. No M is D.
III. Some X are not D.
Option 1: Only conclusions II and III follow
Option 2: Only conclusion III follows
Option 3: All the conclusions follow
Option 4: None of the conclusions follow
Correct Answer: None of the conclusions follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
All X are D – From the above diagram, it is clear that circles of X and D are independent. The diagram doesn't define any relation between them. So this conclusion doesn't follow.
Conclusion II:
No M is D – From the above diagram, it is clear that circles of M and D are overlapping which means some M is D or vice versa but we can't say that no M is D from the positive statement as it doesn't define the relation of no between them. So, this conclusion doesn't follow.
Conclusion III:
Some X are not D – From the above diagram, it is clear that circles of X and D are independent. The diagram doesn't define any relation between them. So this conclusion doesn't follow.
So, none of the conclusions follows. Hence, the fourth option is correct.
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