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Statements: Some keys are locks. All locks are doors. Conclusion: I. Some keys are doors. II. All doors are locks.
Only I follows
Only II follows
Both follow
Neither follows
Only I follows
Use the subset rule: if some A are B and all B are C, the overlapping region of A and B is automatically inside C.
Use the subset rule: if some A are B and all B are C, the overlapping region of A and B is automatically inside C.
Analyze Statement 1
Some keys are locks creates an intersection between the set of keys and the set of locks.
Analyze Statement 2
All locks are doors places the entire set of locks completely inside the set of doors.
Evaluate Conclusion I
Since the overlapping keys-locks region lies within the doors set, Some keys are doors is logically true.
Evaluate Conclusion II
All doors are locks is false because containment is one-way (locks to doors), not vice-versa.
B: Only II follows is wrong because conclusion II is invalid. C: Both follow is wrong because conclusion II is incorrect. D: Neither follows is wrong because conclusion I is correct.
A is correct because the subset of keys that are locks falls inside the doors set, making conclusion I follow while conclusion II is unsupported.
Never reverse a universal quantifier like 'all locks are doors' to 'all doors are locks' unless an explicit equivalence is given.
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