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:
All oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
Option 1: Only conclusions I and III follow
Option 2: Only conclusions II and III follow
Option 3: All conclusions follow
Option 4: Only conclusions I and II follow
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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 fruits are apples – From the Venn diagram, it is evident that the circles representing fruits and apples overlap and have a part of their area in common. So, it can be concluded that some fruits are apples.
Conclusion (II):
Some apples are bananas – From the Venn diagram, it is evident that the circles representing apples and bananas overlap and have a part of their area in common. So, it can be concluded that some apples are bananas.
Conclusion (III):
Some oranges are fruits – From the Venn diagram, it is evident that the circles representing oranges and fruits overlap and have a part of their area in common. So, it can be concluded that some oranges are fruits.
So, all conclusions follow. Hence, the third option is correct.
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