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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 watches are perfumes. No watch is a tie. Conclusions: (I) All perfumes are watches. (II) No perfume is a tie.
Only conclusion I follows
Only conclusion II follows
Neither conclusion I nor II follows
Both conclusions I and II follow
Only conclusion II follows
Visualize Venn diagrams: All A are B means A is inside B. No A is C means A and C have no intersection. Use these to check if conclusions overlap.
Visualize Venn diagrams: All A are B means A is inside B. No A is C means A and C have no intersection. Use these to check if conclusions overlap.
Analyze the Statements
Statement 1: 'All watches are perfumes' means the set of watches is contained entirely within the set of perfumes. Statement 2: 'No watch is a tie' means there is no overlap between the set of watches and the set of ties.
Evaluate Conclusion (I)
Conclusion (I) 'All perfumes are watches' is incorrect because while all watches are perfumes, the reverse is not necessarily true. There can be perfumes that are not watches.
Evaluate Conclusion (II)
Conclusion (II) 'No perfume is a tie' is also incorrect. Since we only know that watches are not ties, there is no restriction preventing other perfumes (those not belonging to the watch set) from being ties.
A: Wrong because neither conclusion is necessarily true. C: Incorrect as only conclusion I is stated, which we proved false. D: Incorrect as only conclusion II is stated, which we proved false.
B is correct because neither conclusion logically follows from the premises given, as the statements do not establish a universal negative relationship between 'perfumes' and 'ties'.
In Syllogism, remember that 'No A is B' only restricts A and B; it never places restrictions on the larger sets that contain A or B unless specifically stated.
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