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 roomsOptionsOnly II follow. Only I follow.NoneOnly I and III follow.Only II and IV 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 roomsOptionsOnly II follow. Only I follow.NoneOnly I and III follow.Only II and IV follow.
Solution
The correct answer is "Only II and IV 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.
Conclusions:
I. All hotels being locks is a possibility - This is not necessarily true. Since no room is a hotel and some keys (which are locks) are doors (which are rooms), it's possible that some locks are not hotels.
II. No lock is a door - This is not true. Some keys are doors and all keys are locks, so some locks are doors.
III. No hotel is a door - This is true. Since no room is a hotel and all doors are rooms, no hotel is a door.
IV. At least some keys are rooms - This is true. Some keys are doors and all doors are rooms, so some keys are rooms.
So, only conclusions II and IV follow from the given statements.
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