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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 slippers are shoes. Some shoes are belts. Conclusions: (I) Some belts are slippers. (II) No belt is a slipper.
Only conclusion (II) follows
Neither conclusion (I) nor (II) follows
Both conclusions (I) and (II) follow
Only conclusion (I) follows
Neither conclusion (I) nor (II) follows
In syllogisms with two 'Some' premises, there is no direct link between the first and last terms unless explicitly stated. Thus, both positive and negative definite conclusions are uncertain, leading to the neither/nor case.
In syllogisms with two 'Some' premises, there is no direct link between the first and last terms unless explicitly stated. Thus, both positive and negative definite conclusions are uncertain, leading to the neither/nor case.
Analyze Statements
Statement 1: 'Some slippers are shoes' creates a partial overlap between the Slipper set and Shoe set. Statement 2: 'Some shoes are belts' creates a partial overlap between the Shoe set and Belt set.
Evaluate Conclusions
The statements do not provide any information regarding a direct relationship between 'slippers' and 'belts'. They could overlap, or they might be completely separate. Therefore, 'Some belts are slippers' is not necessarily true, and 'No belt is a slipper' is also not necessarily true.
Apply Complementary Pair Logic
Since we have a possibility of overlap (Some) and a possibility of no overlap (None) between the same two entities, one must be true in reality, but neither can be logically deduced as definitively true based ONLY on the provided statements. Thus, neither follows.
A: Incorrect because 'Some' is not guaranteed. B: Incorrect because 'No' is not guaranteed. D: Incorrect because 'Some' is not guaranteed.
C is correct because there is no direct logical connection established between 'slippers' and 'belts' in the statements, making both definitive conclusions invalid.
In syllogisms, if two categories are linked to a common middle term but not to each other, all direct relations between those two categories are 'possibilities', not 'certainties', and thus do not 'follow' logically.
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