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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 apples are mangoes. Some mangoes are lemons. Conclusions: (I) At least some mangoes are apples. (II) Some apples are lemons.
Only conclusion II follows
Neither conclusion I nor II follows
Both conclusions I and II follow
Only conclusion I follows
Only conclusion I follows
Visualize Venn diagrams: Since 'All A are M', A is inside M. Since 'Some M are L', the L circle intersects the M circle. Check if the conclusion is definitely true in all scenarios.
Visualize Venn diagrams: Since 'All A are M', A is inside M. Since 'Some M are L', the L circle intersects the M circle. Check if the conclusion is definitely true in all scenarios.
Analyze Statement 1
All apples are mangoes: This means the entire set of 'Apples' lies within the set of 'Mangoes'. Therefore, any 'Apple' is automatically a 'Mango'.
Analyze Statement 2
Some mangoes are lemons: This implies a partial overlap between the 'Mangoes' set and the 'Lemons' set.
Evaluate Conclusions
(I) At least some mangoes are apples: Since all apples are inside the mango set, this must be true. (II) Some apples are lemons: The statements do not provide a direct link between apples and lemons. While it is possible, it is not definitely true.
A: Incorrect because II is not definite. B: Incorrect because I is definite. C: Incorrect because I follows.
D is correct because Conclusion I follows directly from the definition of 'All A are M', while Conclusion II cannot be definitively established from the given statements.
In Syllogism, always look for the 'Possibility' vs 'Definite Truth'. If a relationship isn't explicitly defined (like Apples and Lemons), the conclusion is considered false.