In each of the questions below three statements are given followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: All Train is Bus
No Truck is Auto
Only a few Truck are Bus
Conclusions: I. All Bus being Auto is a possibility
II. All Train being Auto is a possibility
III. Some Bus is not Auto
Correct Answer :
Only II and III follow
Solution :
To determine which conclusions logically follow from the given statements, let us analyze the relationships between the categories step-by-step.
Given Statements:
1. All Train is Bus.
2. No Truck is Auto.
3. Only a few Truck are Bus.
Step 1: Breakdown of Statements
• "All Train is Bus" means the entire circle/category of Train is strictly inside the circle of Bus.
• "No Truck is Auto" means Truck and Auto are completely disjoint sets (0% overlap).
• "Only a few Truck are Bus" implies two things simultaneously:
a) Some Truck are Bus.
b) Some Truck are NOT Bus. (Thus, the intersection of Truck and Bus exists, but Truck is not entirely inside Bus).
Step 2: Evaluating Conclusion I
"All Bus being Auto is a possibility"
From Statement 3, some part of Bus belongs to Truck (since "Only a few Truck are Bus" means there is an overlap between Truck and Bus).
From Statement 2, no Truck can ever be Auto.
Therefore, the portion of Bus that overlaps with Truck can NEVER be Auto.
Hence, it is impossible for all Bus to be Auto.
Conclusion I does NOT follow.
Step 3: Evaluating Conclusion II
"All Train being Auto is a possibility"
We know that all Train is inside Bus. However, the statements do not force Train to overlap with the "Truck" portion of Bus.
Train can lie entirely within the non-Truck portion of Bus.
Since the non-Truck portion of Bus has no restrictions regarding Auto, it is entirely possible for all Trains to be placed inside Auto without violating any statement.
Conclusion II follows.
Step 4: Evaluating Conclusion III
"Some Bus is not Auto"
As analyzed in Step 2, the portion of Bus that overlaps with Truck can never be Auto (because No Truck is Auto).
Since there exists a definite overlap of Bus with Truck, those specific Buses are guaranteed to NOT be Auto.
Thus, "Some Bus is not Auto" is a definite truth.
Conclusion III follows.
Conclusion:
Only conclusions II and III logically follow from the given statements.
The correct answer is Only II and III follow.
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