Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
I. Some buses are motorbikes.
II. All motorbikes are vans.
III. All buses are cars.
Conclusions:
I. Some cars are vans.
II. Some vans are buses.
III. Some vans are motorbikes.
Option 1: Only conclusion II follows
Option 2: All conclusions I, II and III follow
Option 3: Only conclusion I follows
Option 4: Both conclusions I and II follow
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Correct Answer: All conclusions I, II and III follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some cars are vans – From the Venn diagram, we can see that the two circles representing cars and vans intersect and have a common area between them. So, this conclusion follows.
Conclusion (II):
Some vans are buses – From the Venn diagram, we can see that the two circles representing vans and buses intersect and have a common area between them. So, this conclusion follows.
Conclusion (III):
Some vans are motorbikes – From the Venn diagram, we can see that the circle representing motorbikes is completely inside the circle representing vans. So, some vans are motorbikes is a true conclusion.
So, all conclusions I, II, and III follow. Hence, the second option is correct.
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