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Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements. Statements: Some doors are locks. No lock is a key. Conclusions: (I) No door is a key. (II) Some locks are doors.
Neither conclusion I nor II follows
Both conclusions I and II follow
Only conclusion I follows
Only conclusion II follows
Only conclusion II follows
In syllogisms with 'Some A are B' and 'No B is C', A and C have an indeterminate relationship, so 'No A is C' cannot be definitively concluded.
In syllogisms with 'Some A are B' and 'No B is C', A and C have an indeterminate relationship, so 'No A is C' cannot be definitively concluded.
Analyze Statement 1
Some doors are locks. This implies an overlapping region between the set of Doors and the set of Locks.
Analyze Statement 2
No lock is a key. This defines a complete separation between the set of Locks and the set of Keys.
Evaluate Conclusion I
No door is a key. Since only the 'lock' part of the door is restricted from being a key, other parts of 'door' could potentially overlap with 'key'. Thus, it does not logically follow.
Evaluate Conclusion II
Some locks are doors. If 'Some doors are locks' is true, then conversely, 'Some locks are doors' must also be true. This follows.
A: Only II follows, so I is wrong; B: Neither is wrong as II follows; C: Both are wrong as I does not follow.
D is correct because only the conversion of the first statement (Some locks are doors) is a valid conclusion, while the first conclusion about doors and keys cannot be determined.
In syllogisms, remember that 'Some A are B' always converts to 'Some B are A'. However, 'No A is B' does not necessarily make 'No A is C' true if C is a separate set.
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