Question : Directions: Two 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:
No truck is a bus.
Some buses are cars.
Conclusions:
I. No bus is a truck.
II. All cars are trucks.
III. Some cars are buses.
Option 1: Conclusions I, II, and III follow
Option 2: Both conclusions II and III follow
Option 3: Both conclusions I and II follow
Option 4: Both conclusions I and III follow
Correct Answer: Both conclusions I and III follow
Solution : The possible Venn diagram according to the statement is as follows –
Let's analyse the conclusions –
Conclusion I:
No bus is a truck – From the Venn diagram, it is evident that there is a negative relation between a truck and a bus. So, from this, it can be concluded that no bus is a truck. Thus, this conclusion follows.
Conclusion II:
All cars are trucks – Since no bus is a truck and some cars are buses. So, all cars can never be trucks. Thus, this conclusion does not follow.
Conclusion III:
Some cars are buses – From the Venn diagram, it is evident that the circles representing cars and buses overlap and have some parts of their area in common. So, it can be concluded that some cars are buses. Thus, this conclusion follows.
So, both conclusions I and III follow. Hence, the fourth option is correct.
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