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 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. All fruits are vegetables.
II. All vegetables are almonds.
Conclusions:
I. Some vegetables are fruits.
II. All almonds are vegetables.
III. Some fruits are almonds.
Option 1: Both conclusions II and III follow
Option 2: All conclusions follow
Option 3: Both conclusions I and II follow
Option 4: Both conclusions I and III follow
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Correct Answer: Both conclusions I and III follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some vegetables are fruits – From the Venn diagram, it is evident that some parts of the circle representing vegetables lie outside the circle representing fruits while some lie inside. So, from this, it can be concluded that some vegetables are fruits. Thus, this conclusion follows.
Conclusion (II):
All almonds are vegetables – From the Venn diagram, it is evident that some parts of the circle representing almonds lie outside the circle representing vegetables while some lie inside. So, from this, it can be concluded that some almonds are vegetables. Thus, this conclusion does not follow.
Conclusion (III):
Some fruits are almonds – From the Venn diagram, it is evident that all fruits are almonds, So, some fruits will definitely be almonds. So, it can be concluded that some fruits are almonds. Thus, this conclusion follows.
So, both conclusions I and III follow. Hence, the fourth option is correct.
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