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In the following question, two statements are followed by four conclusions. You have to assume the given statements to be true, even if they seem to be at variance with commonly known facts. Read the conclusions carefully and then decide which of the given conclusions logically follows from the statements.
Statements:
All keys are metal objects.
No metal object is edible.
Conclusions:
I. No key is edible
II. Some keys are edible
III. All edible things are keys
IV. Cannot say
I only
Both II and III
Both I and II
IV only
I only
Since all keys are metal and no metal is edible, any key must necessarily be non-edible (Transitive property: A in B, B excluded from C implies A excluded from C).
Since all keys are metal and no metal is edible, any key must necessarily be non-edible (Transitive property: A in B, B excluded from C implies A excluded from C).
Analyze the Statements
Statement 1: All Keys (K) are Metal Objects (M). This means the circle for K is inside the circle for M. Statement 2: No Metal Object (M) is Edible (E). This means the circle for M and the circle for E are separate and do not touch.
Derive Logical Deductions
Since K is inside M, and M has no overlap with E, it follows that K also cannot have any overlap with E. Therefore, No Key is Edible is true.
Evaluate Conclusions
Conclusion I follows directly. Conclusion II is false because no key can be edible. Conclusion III is false because there is no evidence that all edible things must be keys. Conclusion IV is invalid as I is definitely true.
B: II and III are both false because II contradicts the negative relationship and III is not supported by the premises. C: II is false, making the whole option incorrect. D: IV is incorrect because conclusion I is logically certain.
A is correct because the transitive exclusion between keys and edible items is a direct logical consequence of the given universal negative statement.
In Syllogisms, always draw the 'No' relationship as two disjoint circles to prevent accidental overlaps during complex premise mapping.
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