Which of the following statements are logically equivalent? Choose the correct answer from the options given below.

1.All non-trees are non-animals

2.No animals are trees

3.Some animals are not trees

4.No trees are animals

A1 and 4 only

B1 and 2 only

C2 and 4 only ✓ Correct

D2 and 3 only

Correct answer: (C) 2 and 4 only

Explanation

Statements 2 and 4 are equivalent because an E proposition converts without loss.

Statement 2 is 'No animals are trees' and Statement 4 is 'No trees are animals'.

Both are universal negative (E) propositions of the form No S are P.

Simple conversion of an E proposition interchanges subject and predicate while keeping truth value.

So denying overlap from either side asserts exactly the same fact.

The equivalence rests on the valid conversion of the E form.

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