Question : Directions: Three statements are given followed by three conclusions numbered I, II, and III.Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some apples are fruits.
All fruits are vegetables.
No vegetable is healthy.
Conclusions:
I. No apple is healthy.
II. No healthy is vegetable.
III. Some vegetables are apples.
Option 1: Only conclusions I and II follow
Option 2: Only conclusions I and III follow
Option 3: All conclusions follow
Option 4: Only conclusions II and III follow
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Correct Answer: Only 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):
No apple is healthy – From the Venn diagram, it is evident that there is no direct relation between apples and healthy. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (II):
No healthy is vegetable – From the Venn diagram, it is evident that there is a negative relation between healthy and vegetables. So, it can be concluded that no healthy is vegetable.
Conclusion (III):
Some vegetables are apples – From the Venn diagram, it is evident that the two circles representing vegetables and apples overlap and have a part of their area in common. So, it can be concluded that some vegetables are apples.
So, only conclusions II and III follow. Hence, the fourth option is correct.
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