Statements:All windows are doors.All entrances are windows.No gate is a door.Conclusions:I. At least some windows are gates.II. No gate is an entrance.if only conclusion I follows.if only conclusion II follows.if either conclusion I or conclusion II follows.if neither conclusion I nor conclusion II follows.if both conclusion I and conclusion II follow
Question
Statements:All windows are doors.All entrances are windows.No gate is a door.Conclusions:I. At least some windows are gates.II. No gate is an entrance.if only conclusion I follows.if only conclusion II follows.if either conclusion I or conclusion II follows.if neither conclusion I nor conclusion II follows.if both conclusion I and conclusion II follow
Solution
The answer is: if only conclusion II follows.
Here's the step by step reasoning:
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All windows are doors: This means that whatever is a window is also a door.
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All entrances are windows: This means that whatever is an entrance is also a window, and since all windows are doors, all entrances are also doors.
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No gate is a door: This means that gates and doors are mutually exclusive, they have no overlap.
Conclusion I: At least some windows are gates. This is not possible because we know from the statements that no gate is a door, and all windows are doors. So, there can't be any overlap between windows and gates. So, conclusion I does not follow.
Conclusion II: No gate is an entrance. This is true because all entrances are doors (from statement 2 and 1), and no gate is a door (from statement 3). So, there can't be any overlap between gates and entrances. So, conclusion II follows.
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