Which of the following propositions are logically equivalent?

1.No dogs are aggressive animals

2.No aggressive animals are dogs

3.All dogs are non-aggressive

4.Some dogs are not aggressive animals

A3 & 4 only

B1 & 4 only

C1, 2 & 3 only ✓ Correct

D2 & 4 only

Correct answer: (C) 1, 2 & 3 only

Explanation

Statements 1, 2 and 3 all express the same universal negative content.

Statement 1 is No dogs are aggressive animals, an E proposition.

Statement 2 is its converse, No aggressive animals are dogs, and E converts validly.

Statement 3 is its obverse, All dogs are non-aggressive, which is logically equal.

Statement 4 is only the weaker particular O and is not equivalent.

Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.