Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow(s) the given statements.
Statements:
All trains are buses.
Some buses are cars.
Conclusions:
I. All cars are buses.
II. Some buses are trains.
Neither conclusion I nor II follows
Only conclusion II follows
Both the conclusions follow
Only conclusion I follows
Only conclusion II follows
To determine which conclusion(s) follow from the given statements, we can analyze them step-by-step using Venn diagrams or logical deduction.
Step 1: Analyze Statement 1 ("All trains are buses")
This statement means that the class of 'trains' is completely contained within the class of 'buses'. If we draw a circle representing 'trains', it must lie entirely inside the circle representing 'buses'.
Step 2: Analyze Statement 2 ("Some buses are cars")
This statement means that there is an intersection between the circle representing 'buses' and the circle representing 'cars'. However, we do not have any definite information about the relationship between 'cars' and 'trains'; they may or may not overlap.
Step 3: Evaluate Conclusion I ("All cars are buses")
From Statement 2, we only know that some buses are cars, which means some cars are buses. We cannot conclude that all cars are buses. Therefore, Conclusion I does not follow.
Step 4: Evaluate Conclusion II ("Some buses are trains")
From Statement 1, we know that all trains are buses. Since there is at least one train (assuming non-empty sets) and all trains are inside the bus category, it is guaranteed that the portion of buses that contain trains makes "some buses are trains" definitely true. Therefore, Conclusion II follows.
Thus, only conclusion II follows.