Which of the following statements is contrapositive to the following statement - "Some dogs are not aggressive animals"?
Some non-aggressive animals are not non-dogs.
Concept: "Some dogs are not aggressive animals" is a particular negative (O-type) proposition: Some S are not P, where S = dogs and P = aggressive animals. Contraposition is an immediate inference in which we replace the subject with the complement of the predicate and the predicate with the complement of the subject. For an O proposition, contraposition is valid:
Some S are not P → Some non-P are not non-S.
Working: Here non-P = non-aggressive animals and non-S = non-dogs. Substituting gives "Some non-aggressive animals are not non-dogs." This preserves the O form (Some ... are not ...) and correctly complements both terms.
Why the other choices are wrong:
- "Some aggressive animals are not dogs" merely swaps the original terms (a conversion-like move); an O proposition cannot be validly converted.
- "Some dogs are aggressive animals" changes quality from negative to affirmative, so it is not equivalent to the original.
- "Some non-dogs are aggressive animals" is affirmative and complements only one term, so it is not the contrapositive.
Takeaway: Contrapositive of "Some S are not P" is "Some non-P are not non-S" — both terms are negated and their positions exchanged, keeping the particular-negative form.
Correct answer: Some non-aggressive animals are not non-dogs.
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