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Statement: 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 II follow.NoneOnly I and III follow.Only II and IV follow.

Question

Statement: 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 II follow.NoneOnly I and III follow.Only II and IV follow.

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Solution

The given statements can be interpreted as follows:

  1. Some keys are doors: This implies that there is an intersection between the set of keys and the set of doors.
  2. All keys are locks: This implies that the set of keys is a subset of the set of locks.
  3. All doors are rooms: This implies that the set of doors is a subset of the set of rooms.
  4. No room is a hotel: This implies that there is no intersection between the set of rooms and the set of hotels.

Now, let's analyze the conclusions:

I. All hotels being locks is a possibility: This is possible because there is no statement that directly contradicts this. The fact that no room is a hotel does not mean that a hotel cannot be a lock.

II. No lock is a door: This is false because some keys are doors and all keys are locks. Therefore, some locks must be doors.

III. No hotel is a door: This is true because all doors are rooms and no room is a hotel. Therefore, no door can be a hotel.

IV. At least some keys are rooms: This is true because some keys are doors and all doors are rooms. Therefore, some keys must be rooms.

So, the correct answer is "Only I, III and IV follow".

This problem has been solved

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