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Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements. Statements: All ovals are bins. No bin is a car. No bin is a plum. Conclusions: (I): No oval is a car. (II): Some plums are cars.
Neither conclusion (I) nor (II) follows.
Both conclusions (I) and (II) follow.
Only conclusion (II) follows.
Only conclusion (I) follows.
Only conclusion (I) follows.
Draw standard Venn diagrams or use the rules of conversion: 'All A are B' means A inside B. 'No B is C' means complete separation. If A is inside B and B has zero overlap with C, then A also has zero overlap with C (No A is C).
Draw standard Venn diagrams or use the rules of conversion: 'All A are B' means A inside B. 'No B is C' means complete separation. If A is inside B and B has zero overlap with C, then A also has zero overlap with C (No A is C).
Step 1: Analyze Statement 1 (All ovals are bins)
The entire set of 'Ovals' is completely enclosed inside the set of 'Bins'. Mathematically, Oval тКВ Bin.
Step 2: Analyze Statement 2 and 3 (No bin is a car, No bin is a plum)
The set of 'Bins' has zero intersection with the set of 'Cars' and the set of 'Plums'.
Step 3: Evaluate Conclusion I (No oval is a car)
Since all Ovals are inside Bins, and Bins have no overlap with Cars, Ovals also cannot have any overlap with Cars. Thus, Conclusion I definitely follows.
Step 4: Evaluate Conclusion II (Some plums are cars)
There is no direct or indirect positive statement connecting Plums and Cars. They are both separate negative entities relative to Bins. Thus, Conclusion II does not follow definitively.
A: Incorrect because Conclusion I logically follows from the statements. B: Incorrect because Conclusion II is not supported by the statements. C: Incorrect because Conclusion I is valid while Conclusion II is invalid.
D is correct because since all ovals are inside bins and no bin is a car, no oval can be a car (Conclusion I follows), whereas there is no given relation between plums and cars (Conclusion II does not follow).
In negative syllogism statements (No A is B), remember that any subset inside A is also completely excluded from B.
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