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Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:

All keys are windows.

No window is a door.

Some doors are locks.

Conclusions:

I. Some locks are keys.

II. No lock is a window.

III. No door is a key.

  1. A
    Both conclusions I and II follow.
  2. B
    Only conclusion II follows.
  3. C
    Only conclusion I follows.
  4. D
    Only conclusion III follows.

Solution & Step-by-step Explanation

Let's analyze the statements using Venn diagrams or logical rules:
All keys are windows → The set of keys is completely inside the set of windows.

No window is a door → The set of windows and the set of doors do not intersect at all. Since all keys are inside windows, no key can be a door either.

Some doors are locks → There is an intersection between doors and locks.

Now let's evaluate the conclusions:

Conclusion I: Some locks are keys. Since locks overlap with doors, and doors are completely separated from windows (and thus keys), locks do not necessarily intersect with keys. This is not definitely true.

Conclusion II: No lock is a window.
Some locks are doors, and no door is a window. However, the remaining part of locks could potentially overlap with windows in a possible case. Thus, it is not definitely true in all cases.

Conclusion III: No door is a key.
Since all keys are inside windows, and no window is a door, it is absolutely certain that no key can be a door, which means no door is a key. This conclusion is definitely true.

Therefore, only conclusion III follows.

Practice this question

Try it yourself before checking the explanation above.

Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:

All keys are windows.

No window is a door.

Some doors are locks.

Conclusions:

I. Some locks are keys.

II. No lock is a window.

III. No door is a key.
A
Both conclusions I and II follow.
B
Only conclusion II follows.
C
Only conclusion I follows.
D
Only conclusion III follows.

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