Select the correct answerStatement: Some keys are doorsAll keys are locks.All doors are roomsNo room is a hotelConclusions:I. All hotels being locks is a possibility II. No lock is a door III. No hotel is a doorIV. At least some keys are roomsOptions Only I follow.Only I and III follow.NoneOnly II and IV follow.Only II follow.
Question
Select the correct answerStatement: Some keys are doorsAll keys are locks.All doors are roomsNo room is a hotelConclusions:I. All hotels being locks is a possibility II. No lock is a door III. No hotel is a doorIV. At least some keys are roomsOptions Only I follow.Only I and III follow.NoneOnly II and IV follow.Only II follow.
Solution
The correct answer is "Only I and III follow."
Here's the step-by-step reasoning:
Statement: Some keys are doors. All keys are locks. All doors are rooms. No room is a hotel.
Conclusion I: All hotels being locks is a possibility. This is true because there is no direct relationship between hotels and locks mentioned in the statements, so it's possible.
Conclusion II: No lock is a door. This is false because according to the first two statements, some keys are doors and all keys are locks, which means some locks are doors.
Conclusion III: No hotel is a door. This is true because all doors are rooms and no room is a hotel, so no hotel can be a door.
Conclusion IV: At least some keys are rooms. This is false because while some keys are doors and all doors are rooms, it doesn't necessarily mean that those specific keys that are doors are also rooms.
So, only conclusions I and III follow the statements.
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