Which of the following statements are logically equivalent?
A. Some cricketers are kind men.
B. Some kind men are cricketers.
C. Some cricketers are not non-kind men.
D. Some non-kind men are not non-cricketers.
Choose the correct answer from the options given below:
A, B and C only
We test logical equivalence using two rules of traditional categorical logic: conversion and obversion.
Statement A: "Some cricketers are kind men" is a particular affirmative statement.
Rule 1 - Conversion: For any particular affirmative statement of the form "Some X are Y", simply swapping the two terms gives an equivalent statement "Some Y are X" (this is called simple conversion, and it is always valid for particular affirmative statements). Applying this to A: "Some cricketers are kind men" becomes "Some kind men are cricketers" — which is exactly Statement B. So A and B are logically equivalent.
Rule 2 - Obversion: For any statement, you can obtain an equivalent statement by changing it from affirmative to negative (or negative to affirmative) and replacing the predicate term with its opposite/complement. For a particular affirmative statement "Some X are Y", the obverse is "Some X are not non-Y". Applying this to A: "Some cricketers are kind men" obverts to "Some cricketers are not non-kind men" — which is exactly Statement C. So A and C are logically equivalent.
Since A is equivalent to both B and C, all three — A, B, and C — are logically equivalent to each other.
Now check Statement D: "Some non-kind men are not non-cricketers". Obverting this gives "Some non-kind men are cricketers". Converting this gives "Some cricketers are non-kind men", which talks about cricketers who are NOT kind. This is the opposite quality from Statement A ("Some cricketers ARE kind men"), so D is a different statement and is not part of the equivalence group.
Therefore, only A, B and C are logically equivalent
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