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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 lakes are rivers. Some rivers are ponds. Conclusions: (I) Some lakes are ponds. (II) Some ponds are not rivers.
Both conclusions I and II follow
Neither conclusion I nor II follows
Only conclusion II follows
Only conclusion I follows
Neither conclusion I nor II follows
Represent the statements as overlapping circles. 'Some' means an intersection exists; if the circles for two groups don't HAVE to touch, the conclusion is false.
Represent the statements as overlapping circles. 'Some' means an intersection exists; if the circles for two groups don't HAVE to touch, the conclusion is false.
Analyze Statement 1
Some lakes are rivers. This means there is an intersection between the set of Lakes and Rivers.
Analyze Statement 2
Some rivers are ponds. This means there is an intersection between the set of Rivers and Ponds.
Evaluate Conclusions
Conclusion I (Some lakes are ponds) is not necessarily true because the connection between Lakes and Ponds is not explicitly stated. Conclusion II (Some ponds are not rivers) is not necessarily true because it is possible that all ponds are part of the river group.
A: Incorrect as it assumes a relationship not stated. C: Incorrect as it contradicts the logical possibility of either statement holding true. D: Incorrect as only conclusion II is not guaranteed.
Neither conclusion I nor II follows is the correct logical deduction because there is no direct or necessary relationship established between Lakes and Ponds, and it is possible for all Ponds to be Rivers.
In syllogisms, 'Some' does not imply a universal connection; always look for the possibility of a 'counter-example' drawing to disprove a conclusion.
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