Which of the following statements are logically equivalent?

1.No lions are herbivorous animals

2.No herbivorous animals are lions

3.All lions are non-herbivorous animals

4.All non-herbivorous animals are non-lions

A2, 3 & 4 only

B3 & 4 only

C2 & 4 only

D1, 2 & 3 only ✓ Correct

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

Explanation

The E proposition No lions are herbivorous, its converse, and its obverse all say the same thing.

Conversion of an E is valid, giving No herbivorous animals are lions as Statement 2.

Obversion of the E gives All lions are non-herbivorous animals as Statement 3.

Both these transformations preserve truth value exactly, so Statements 1, 2 and 3 are equivalent.

Statement 4 reduces to All lions are herbivorous, which is not equivalent.

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