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

1.All pens are non-pencils.

2.All non-pencils are pens.

3.No pencils are pens.

4.No pens are pencils.

A2 & 4 only

B1 & 2 only

C2, 3 & 4 only

D1, 3 & 4 only ✓ Correct

Correct answer: (D) 1, 3 & 4 only

Explanation

Statements 1, 3 and 4 are logically equivalent.

Take "No pens are pencils" as the base universal negative.

Its converse, since a universal negative converts simply, is "No pencils are pens", which is Statement 3.

Its obverse is "All pens are non-pencils", which is Statement 1.

Simple conversion and obversion both preserve truth, so these three coincide.

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