Which of the following is contradictory to the statement—"No birds are mammals"?

Concept

In the traditional square of opposition, a universal negative (E) proposition, ‘No S are P,’ and a particular affirmative (I) proposition, ‘Some S are P,’ are contradictories. Contradictories cannot both be true and cannot both be false.

Application

1. Classify the given statement: ‘No birds are mammals’ is a universal negative (E) proposition, with birds as the subject class and mammals as the predicate class.

2. Form its contradictory by changing both quantity (universal to particular) and quality (negative to affirmative): ‘Some birds are mammals.’

3. This proposition asserts that at least one individual belongs to both classes, directly denying that their intersection is empty.

Cross-check and contrast

In set terms, ‘No birds are mammals’ says B ∩ M = ∅. Its negation is B ∩ M ≠ ∅, expressed by ‘Some birds are mammals.’

• ‘Some birds are not mammals’ is the particular negative (O) form; it allows an instance outside the mammal class rather than asserting an overlap.

• ‘All birds are mammals’ is the universal affirmative (A) form; it is a contrary of the universal negative in the traditional square, not its contradictory.

• ‘All mammals are birds’ reverses the subject and predicate classes, so it is not the direct negation of the given statement.

Therefore, ‘Some birds are mammals’ is the contradictory statement.