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In the following question, two statements are followed by two conclusions. You have to assume the given statements to be true, even if they seem to be at variance with commonly known facts. Read both the conclusions and then decide which of the given conclusions logically follows from the statements.
Statements:
All buses are vehicles.
Some vehicles are cars.
Conclusions:
I. All cars are buses.
II. Some cars are vehicles.
Only conclusion I follows
Only conclusion II follows
Both conclusions I and II follow
Neither conclusion I nor II follows
Only conclusion II follows
Apply the converse rule for 'Some': 'Some A are B' always implies 'Some B are A', allowing immediate validation of conclusion II.
Apply the converse rule for 'Some': 'Some A are B' always implies 'Some B are A', allowing immediate validation of conclusion II.
Analyze Statement 1
All buses are vehicles: This implies that the set of buses is entirely contained within the set of vehicles.
Analyze Statement 2
Some vehicles are cars: This implies there is an intersection between the set of vehicles and the set of cars. It does not establish a relationship between buses and cars.
Evaluate Conclusions
Conclusion I (All cars are buses) is not necessarily true as there is no link between cars and buses. Conclusion II (Some cars are vehicles) is the direct converse of 'Some vehicles are cars', which is always true in categorical logic.
A: Incorrect because there is no logical link between buses and cars; C: Incorrect because conclusion I is not necessarily true; D: Incorrect because conclusion II follows logically from the statements.
B is correct because conclusion II is the direct logical converse of the second statement, while conclusion I cannot be deduced.
Always test for the possibility of overlapping sets using a Venn diagram; if a conclusion doesn't hold in all possible diagrams, it is invalid.
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