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:
I. All bikes are cars.
II. Some cars are trucks.
III. All trucks are cycles.
Conclusions:
I. Some cars are cycles.
II. Some cycles are trucks.
III. Some bikes are trucks.
Option 1: Only conclusions II and III follow
Option 2: Only conclusions I and III follow
Option 3: Only conclusions I and II follow
Option 4: All conclusions follow
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Correct Answer: Only conclusions I and II follow
Solution :
The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some cars are cycles – From the Venn diagram, we can see that the circles representing cars and cycles intersect and have a part of their area in common. So, this conclusion follows.
Conclusion (II):
Some cycles are trucks – From the Venn diagram, we can see that the circle representing trucks is completely inside the circle representing cycles. So, this conclusion follows.
Conclusion (III):
Some bikes are trucks – From the Venn diagram, there is no definite relation between bikes and trucks. So, this conclusion does not follow.
So, only conclusions I and II follow. Hence, the third option is correct.
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