In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusion(s) logically follow(s) from the statements.
Statements:
All chairs are doors.
Some doors are keys.
All keys are windows.
Conclusions:
I. All chairs are keys.
II. Some windows are doors.
- ABoth conclusions I and II follow.
- BNeither conclusion I nor II follows.
- COnly conclusion II follows.
- DOnly conclusion I follows.
Solution & Step-by-step Explanation
Let's evaluate the statements logically:
Statements:
All chairs are doors. (Chairs ⊆ Doors)
Some doors are keys. (Doors ∩ Keys
=∅)
All keys are windows. (Keys ⊆ Windows)
Conclusions:
Conclusion I: "All chairs are keys." There is no definite relationship connecting chairs and keys from the premises. Thus, conclusion I does not follow.
Conclusion II: "Some windows are doors." Since some doors are keys, and all keys are windows, the overlapping part of keys and doors is also a part of windows. Hence, some windows are definitely doors. Thus, conclusion II follows.
Therefore, only conclusion II follows.
Statements:
All chairs are doors. (Chairs ⊆ Doors)
Some doors are keys. (Doors ∩ Keys
=∅)
All keys are windows. (Keys ⊆ Windows)
Conclusions:
Conclusion I: "All chairs are keys." There is no definite relationship connecting chairs and keys from the premises. Thus, conclusion I does not follow.
Conclusion II: "Some windows are doors." Since some doors are keys, and all keys are windows, the overlapping part of keys and doors is also a part of windows. Hence, some windows are definitely doors. Thus, conclusion II follows.
Therefore, only conclusion II follows.