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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 wigs are plastics. All stones are plastics. Conclusion: (I) All plastics are wigs. (II) Some wigs are stones.
Only conclusion (II) follows.
Only conclusion (I) follows.
Both conclusions (I) and (II) follow.
Neither conclusion (I) nor (II) follows.
Neither conclusion (I) nor (II) follows.
In syllogisms with all positive statements, no 'some not' or negative conclusions can follow. Since both premises are 'All', only conclusions that follow the universal subset rule or the inherent 'some' relationship between sub-parts can be valid.
In syllogisms with all positive statements, no 'some not' or negative conclusions can follow. Since both premises are 'All', only conclusions that follow the universal subset rule or the inherent 'some' relationship between sub-parts can be valid.
Analyze Premises
Premise 1: 'All wigs are plastics' (Wigs is a subset of Plastics). Premise 2: 'All stones are plastics' (Stones is a subset of Plastics). Both Wigs and Stones are contained within the Plastics set, but they have no defined overlap with each other.
Evaluate Conclusion I
Conclusion: 'All plastics are wigs'. This is the invalid converse of the premise 'All wigs are plastics'. While some plastics are wigs, we cannot conclude that all of them are.
Evaluate Conclusion II
Conclusion: 'Some wigs are stones'. Since the premises only define a relationship between Wigs/Plastics and Stones/Plastics, there is no information linking Wigs and Stones. Thus, this cannot be concluded.
A: Only (II) follows is wrong as (II) is not certain. B: Only (I) follows is wrong as (I) is not certain. C: Both follow is wrong because neither is logically derived from the premises.
D is correct because neither conclusion follows logically from the given statements based on set theory rules.
In Syllogisms, always check if a relationship is 'definitely true' or 'possible'. If a conclusion is only possible but not certain, it is treated as false in strict logical deduction.
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