Statements: - All trains are buses.
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Statements:**
- All trains are buses.
- No room is bus.
- All boats are rooms.
Conclusions:
- I. No boat is train.
- II. No bus is boat.
- III. No train is room.
Which of the following conclusions logically follow from the given statements?
Show answer & explanation
Since all trains are buses and no room is a bus, trains and rooms are completely disjoint (III follows). Since all boats are rooms, boats and buses are completely disjoint (II follows). Consequently, boats and trains are completely disjoint (I follows). All three conclusions follow.
Step-by-step Derivation:
Step 1: Premise 1: Trains in Buses. Premise 2: Rooms and Buses are disjoint. Premise 3: Boats in Rooms.
Step 2: Check Conclusion I (No boat is train): Boats are in Rooms, which is disjoint from Buses, which contains Trains. Thus Boats and Trains are disjoint. Follows.
Step 3: Check Conclusion II (No bus is boat): Buses are disjoint from Rooms, and Boats are inside Rooms. Thus disjoint. Follows.
Step 4: Check Conclusion III (No train is room): Trains are in Buses, which is disjoint from Rooms. Follows.
Step 5: All conclusions follow.