Which of the following statements are logically equivalent?

A. Some animals are herbivores
B. Some non-herbivores are not animals
C. Some animals are non-herbivores
D. Some animals are not non-herbivores

Choose the correct answer from the options given below:

Correct option is D

A. "Some animals are herbivores"

Logical Form:I-type(Some S are P).

D. "Some animals are not non-herbivores"

"Not non-herbivores" =herbivores(double negation).

So, it means: "Some animals are herbivores"(same as A).

Two statements arelogically equivalentif theyalways have the same truth value(i.e., both true or both false in every possible scenario).

Key Tests for Equivalence:

1. Same Meaning:Rephrased versions of the same statement.

   • Example:

     • "Some S are P" ≡ "Some S are not non-P" (double negation).

2. Truth Tables:Columns for both statements match in all cases.

3. Logical Rules:

   • Obversion/Conversion(e.g., "No S are P" ≡ "No P are S").

   • Double Negation(e.g., "Not non-P" = "P").