Question : Directions: In the following question below, some statements are followed by some conclusions. 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 from the given statements.
Statements:
I. All women are hardworking.
II. All intelligent are advocates.
III. Some intelligent are women.
Conclusions:
I. Some advocates are women.
II. Some hardworking are women.
III. Some women are advocates.
IV. Some hardworking are intelligent.
Option 1: Only conclusions II, III, and IV follow
Option 2: Only conclusions I, II, and III follow
Option 3: Only conclusions I, III, and IV follow
Option 4: All conclusions follow
Correct Answer: All conclusions follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some advocates are women – From the Venn diagram, we can see that the circles representing advocates and women intersect and have some areas in common. So, some advocates are women. Therefore, this conclusion follows.
Conclusion (II):
Some hardworking are women – From the Venn diagram, the circle of women is completely inside the circle of hardworking. Therefore, this conclusion follows.
Conclusion (III):
Some women are advocates – From the Venn diagram, we can see that the circles representing advocates and women intersect and have some areas in common. So, some women are advocates. Therefore, this conclusion follows.
Conclusion (IV):
Some hardworking are intelligent – From the Venn diagram, we can see that the circles representing hardworking and intelligent intersect each other and have some areas in common. So, some hardworking are intelligent. Therefore, this conclusion follows.
So, all conclusions follow. Hence, the fourth option is correct.
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