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Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: Some peacocks are robins. All robins are sparrows. All sparrows are owls. Conclusions: (I) No owl is a peacock. (II) All sparrows are peacocks.
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Only conclusion (II) follows
Both conclusions (I) and (II) follow
Neither conclusion (I) nor (II) follows
Identify intersection overlaps: Since all robins and sparrows are owls, and some peacocks are robins, a portion of the peacock population is definitely inside the owl circle, invalidating 'No owl is a peacock' and not proving 'All sparrows are peacocks'.
Identify intersection overlaps: Since all robins and sparrows are owls, and some peacocks are robins, a portion of the peacock population is definitely inside the owl circle, invalidating 'No owl is a peacock' and not proving 'All sparrows are peacocks'.
Establish the Relationships
From statements: (1) Some Peacocks are Robins. (2) All Robins are Sparrows. (3) All Sparrows are Owls. Combined: Peacocks intersect with Robins, and since all Robins are contained within Sparrows, and all Sparrows are contained within Owls, some Peacocks must necessarily be contained within the Owl circle.
Evaluate Conclusion (I)
Conclusion (I) claims 'No owl is a peacock'. However, because some Peacocks are Robins and all Robins are Owls, there exists an overlap between Peacocks and Owls. Thus, (I) is false.
Evaluate Conclusion (II)
Conclusion (II) claims 'All sparrows are peacocks'. The statements only establish that some peacocks are robins/sparrows; there is no information to suggest the entire set of sparrows is contained within the set of peacocks. Thus, (II) is false.
A: (I) is false because some Peacocks are definitely Owls. C: (II) is false as the statements do not indicate the entirety of sparrows are peacocks. D: Both conclusions are false based on the Venn diagram derivation.
B is correct because the overlap between peacocks and owls refutes conclusion (I), and the statements fail to provide sufficient data to support conclusion (II).
In Syllogism, always look for the 'possibility' vs 'definiteness'тАФif an overlap exists, a 'No' statement is automatically invalidated.
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