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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: Some tomatoes are apples. All apples are mushrooms. Conclusions: (I) Some mushrooms are tomatoes (II) All apples are tomatoes
Only conclusion (II) follows
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Only conclusion (I) follows
Visualize Venn diagram: If 'Some A are B' and 'All B are C', then 'Some C are A' (A inside C) and 'Some C are B' must follow. 'All B are A' is not necessarily true.
Visualize Venn diagram: If 'Some A are B' and 'All B are C', then 'Some C are A' (A inside C) and 'Some C are B' must follow. 'All B are A' is not necessarily true.
Analyze Statement 1
Some tomatoes are apples (Intersection exists between Tomato set and Apple set).
Analyze Statement 2
All apples are mushrooms (The entire Apple set is contained within the Mushroom set).
Evaluate Conclusion I
Since some tomatoes are apples, and all apples are mushrooms, the portion of tomatoes that are apples must also be mushrooms. Thus, some mushrooms are tomatoes (TRUE).
Evaluate Conclusion II
The statement only says 'Some tomatoes are apples'. It does not imply that all apples are tomatoes (that would require the reverse 'All apples are tomatoes', which is not stated and not logically forced). (FALSE).
A: Incorrect because conclusion (II) does not logically follow. B: Incorrect because conclusion (I) is valid, making this choice incomplete. D: Incorrect because conclusion (I) definitely follows from the statements.
C is correct because conclusion (I) logically follows from the intersection of the sets, while conclusion (II) is not supported by the given statements.
In Syllogisms, always look for the relationship between the middle term ('apples') to connect the other two categories. Do not assume 'All A are B' implies 'All B are A'.
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