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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: All parrots are rats. Some rats are lambs. No lamb is a horse. Conclusions: (I) All rats are horses. (II) Some lambs are parrots.
Only conclusion (II) follows
Both conclusions (I) and (II) follow
Neither conclusion (I) nor (II) follows
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
Visualize Venn diagrams: If a conclusion requires a relationship not explicitly established by the premises, it is invalid.
Visualize Venn diagrams: If a conclusion requires a relationship not explicitly established by the premises, it is invalid.
Analyze Statement 1 and 2
All parrots are rats (P inside R) and some rats are lambs (R intersects L). Since parrots are inside rats, it is possible for some lambs to be rats, but there is no information indicating any lamb is a parrot.
Analyze Statement 3 and Conclusion 1
No lamb is a horse. Conclusion 1 states all rats are horses. This is clearly false because some rats are lambs, and lambs cannot be horses; thus, at least those rats that are lambs cannot be horses.
Analyze Conclusion 2
Conclusion 2 states some lambs are parrots. Based on the diagrams, parrots are entirely contained within rats, but they have no defined relationship with lambs. Therefore, this conclusion cannot be definitively deduced.
A: Only II is incorrect because there is no link between parrots and lambs. B: Both are incorrect as shown in the steps. D: Only I is incorrect because the statement specifically says some rats are lambs, and lambs are not horses, contradicting the idea that all rats are horses.
C is correct because neither conclusion follows from the given premises as there is no definite link between parrots and lambs, and the statement that all rats are horses contradicts the logic regarding lambs.
In Syllogism, always look for the possibility. If a conclusion is possible but not certain, it is treated as false in these tests.
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