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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 oranges are mangoes. No mango is a banana. Conclusions: (I) No banana is a mango. (II) All mangoes are oranges.
Both conclusions I and II follow
Only conclusion II follows
Only conclusion I follows
Neither conclusion I nor II follows
Only conclusion I follows
In syllogisms with 'All A are B' and 'No B is C', a universal negative relationship (No A is C) is always implied between A and C.
In syllogisms with 'All A are B' and 'No B is C', a universal negative relationship (No A is C) is always implied between A and C.
Analyze Statement 1
All oranges are mangoes: This means the set of 'Oranges' is a subset of the set of 'Mangoes'.
Analyze Statement 2
No mango is a banana: This creates a complete separation between the entire set of 'Mangoes' and the set of 'Bananas'.
Evaluate Conclusions
I) Since no mango is a banana, and all oranges are inside the mango set, no banana can be an orange (or mango). Conclusion I follows. II) 'All mangoes are oranges' is not supported; the statement only guarantees that all oranges are mangoes, not vice-versa. Conclusion II does not follow.
A: Only conclusion I follows is correct; B: Both conclusions follow is incorrect because II is invalid; C: Only conclusion II follows is incorrect because II is invalid and I is valid; D: Neither follows is incorrect because I is logically sound.
Only conclusion I follows is correct because the entire set of mangoes is excluded from bananas, and oranges are contained within the mango set.
In 'All A are B' type statements, remember that the reverse ('All B are A') is a possibility but not a necessity. Always look for the 'Definite' relationship.
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