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
Similar Questions
In a square of opposition, if 'No animals with horns are carnivores' is false, which of the following is the correct code?
codes:
A. 'Some animals with horns are carnivores' is true.
B. 'Some animals with horns are not carnivores' is true.
C. 'All animals with horns are carnivores' is false
D. 'All the animals with horns are carnivores' is undermined.Which of the following statements is contrary to the statement- "No football players are kind-hearted human beings"?
If the statement-"Some athletes are kind human beings" is given as true, then which of the following statements can be immediately inferred to be false?
Important Questions from Classical Square of Opposition
As per square of opposition, if the statement- "All apes are mammals" is given as true, which of the following statements can be immediately inferred to be false?
A. No apes are mammals.
B. Some apes are mammals.
C. Some mammals are apes.
D. Some apes are not mammals.
Choose the correct answer from the options given below:
Which of the following statements are logically equivalent?
A. Some apes are not non-monkeys.
B. Some monkeys are not non-apes.
C. Some monkeys are apes.
D. Some apes are monkeys.
Choose the correct answer from the options given below:
If the statement, 'Some animals are not ferocious' is given as true, then which of the following could be immediately inferred from it:
A. 'All animals are ferocious' is undetermined
B. 'Some animals are ferocious' is false
C. 'No animals are ferocious' is undetermined
D. 'All animals are ferocious' is false
Choose the correct answer from the options given below:
In Classical Square of Opposition, if 'Some S is not P' is true then which of the following could be immediately inferred from it?
A. 'Some S is P' is false
B. 'All S is P' is false
C. 'No S is P' is undetermined
D. 'Some S is P' is undetermined
E. 'All S is P' is undetermined
Choose the correct answer from the options given below:
If the statement "All women are honest" is given as true, what could be immediately inferred from the following?
(A) 'No women are honest' is false
(B) 'Some women are not honest' is true
(C) 'Some women are not honest' is false
(D) 'Some women are honest' is true
Choose the correct answer from the options given below:
