Which of the following statements are logically equivalent?

1.No soaps are writing-tools.

2.All soaps are non-writing-tools.

3.No non-writing-tools are soaps.

4.No writing-tools are soaps.

A1 & 4 only

B1, 2 & 4 only ✓ Correct

C2 & 3 only

D1 & 3 only

Correct answer: (B) 1, 2 & 4 only

Explanation

Statements 1, 2 and 4 are logically equivalent.

Statement 1, 'No soaps are writing-tools', is the universal negative to be tested.

Its obverse, 'All soaps are non-writing-tools', is Statement 2, so they carry the same meaning.

Its converse, 'No writing-tools are soaps', is Statement 4, since the universal negative converts simply.

Statement 3, 'No non-writing-tools are soaps', would imply all soaps are writing-tools, the very reverse, so it is not equivalent.

Hence obversion and simple conversion tie the first, second and fourth together.

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