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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 roses are lilies. No lily is a marigold. Conclusions: (I) All lilies are roses. (II) No rose is a marigold.
Only conclusion II follows
Neither conclusion I nor II follows
Both conclusions I and II follow
Only conclusion I follows
Only conclusion II follows
Visualize Venn diagrams: Since all roses are lilies, they are inside the lily circle. Since the lily circle has zero contact with marigolds, the inner rose circle must also have zero contact with marigolds.
Visualize Venn diagrams: Since all roses are lilies, they are inside the lily circle. Since the lily circle has zero contact with marigolds, the inner rose circle must also have zero contact with marigolds.
Analyze Statement 1
All roses are lilies. This means the set of 'Roses' is a subset of the set of 'Lilies'.
Analyze Statement 2
No lily is a marigold. This establishes that the entire 'Lilies' set is disjoint from the 'Marigold' set.
Evaluate Conclusions
Conclusion I: 'All lilies are roses' is false because while roses are inside lilies, not all lilies are necessarily roses. Conclusion II: 'No rose is a marigold' is true because if no lily touches a marigold, then no rose (which is part of the lily group) can touch a marigold.
Conclusion I is incorrect because the reverse of 'All A are B' is not necessarily 'All B are A'. Options that include I (both conclusions follow or only I follows) are therefore wrong.
B is correct because while Conclusion I is a logically invalid reversal, Conclusion II correctly follows from the fact that Roses are a subset of Lilies, which are entirely excluded from Marigolds.
In syllogisms, remember that 'No A is B' implies 'No B is A'. If you ever see 'All A are B', do not assume 'All B are A' unless specified.
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