Which of the following statement is logically equivalent to "No birds are mammals"?
No mammals are birds.
Concept: 'No birds are mammals' is a universal negative (E-type) proposition. For an E-type proposition, the operation of conversion (interchanging the subject and predicate) yields a statement that is logically equivalent, because 'No S are P' always has the same truth value as 'No P are S'.
Working: Take 'No birds are mammals' (S = birds, P = mammals). Swapping subject and predicate gives 'No mammals are birds'. Since the two classes share no members, the exclusion is mutual, so both statements are true together and false together. Hence 'No mammals are birds' is logically equivalent to the original.
Why the other choices are wrong:
'Some birds are not mammals' is a particular negative; it is merely implied by the original (subalternation) but is weaker and not equivalent, since it could be true even if some birds were mammals.
'Some non-birds are mammals' talks about the complement class of birds and adds new information not contained in the original, so it is not equivalent.
'All non-birds are mammals' is a universal affirmative about a different subject class and is clearly not equivalent (it would even be false in the real world).
Takeaway: An E-proposition can be converted freely without changing its meaning.
Correct answer: No mammals are birds.
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