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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: All cups are plates. All plates are glasses. Conclusions: (I) Some plates are not cups. (II) All cups are glasses.
Only conclusion II follows
Both conclusions I and II follow
Only conclusion I follows
Neither conclusion I nor II follows
Only conclusion II follows
Visualize Venn diagrams: Cups inside Plates, and Plates inside Glasses. Therefore, Cups are also inside Glasses.
Visualize Venn diagrams: Cups inside Plates, and Plates inside Glasses. Therefore, Cups are also inside Glasses.
Analyze Statements
Statements: (1) All Cups are Plates. (2) All Plates are Glasses. This establishes a nested hierarchy: Cups тКВ Plates тКВ Glasses.
Evaluate Conclusion I
Conclusion I: 'Some plates are not cups'. In syllogism rules, 'All A are B' does not necessarily mean 'Some B are not A' if we don't have information about other elements of B. Thus, this cannot be definitively concluded to be true.
Evaluate Conclusion II
Conclusion II: 'All cups are glasses'. Since all Cups are inside the set of Plates, and all Plates are inside the set of Glasses, it logically follows that all Cups are indeed inside the set of Glasses.
I: The statement 'Some plates are not cups' is not necessarily true because the entirety of Plates could theoretically be only Cups (All Plates are Cups); II: This correctly follows from the transitive property of the subset relationship (Cups тКВ Plates тКВ Glasses).
A is correct because conclusion II is a direct logical consequence of the statements, while conclusion I is not necessarily true.
In syllogisms, 'All A are B' never justifies 'Some B are not A' unless 'Some B are not A' is explicitly stated or can be derived from other negative constraints.
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