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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 lemons are potatoes. Some lemons are papayas. Conclusions: (I) Some potatoes are papayas. (II) All papayas are potatoes.
Only conclusion (I) follows
Only conclusion (II) follows
Both conclusions (I) and (II) follow
Neither conclusion (I) nor (II) follows
Only conclusion (I) follows
Convert statements to Venn diagram or standard syllogism rules: All A are B means inside relationship. Some A are B means intersecting relationship. Combine using middle term 'lemons'.
Convert statements to Venn diagram or standard syllogism rules: All A are B means inside relationship. Some A are B means intersecting relationship. Combine using middle term 'lemons'.
Analyze Statement 1
All lemons are potatoes means the entire set of Lemons is contained within Potatoes (Lemon subset of Potato).
Analyze Statement 2
Some lemons are papayas means there is an intersection between the set of Lemons and Papayas.
Evaluate Conclusion I
Since some portion of Potatoes contains Lemons, and those Lemons overlap with Papayas, it must follow that some Potatoes are Papayas. Conclusion (I) is valid.
Evaluate Conclusion II
All papayas are potatoes is not universally given or guaranteed by the statements, as Papayas only intersect with Lemons. Conclusion (II) does not follow.
B: Conclusion II does not follow since universal containment of papayas in potatoes is not established. C: Both cannot follow because conclusion II is invalid. D: Neither cannot be true as conclusion I logically follows.
A is correct because conclusion (I) logically follows from the given statements while conclusion (II) does not.
In affirmative syllogism problems with 'All' and 'Some' statements, partial intersections ('Some A are B') combined with supersets ('All B are C') always validate 'Some A are C'.
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