Which of the following statements are logically equivalent?

A) Some animals are birds.

B) Some animals are not non-birds.

C) Some non-birds are not non-animals.

D) Some birds are animals.

Choose the correct answer from the options given below:

The correct option is A, B and D Only.

Let us analyze each statement to determine their logical equivalence by translating them into standard logical forms using set theory or formal representation:
Let $A$ represent the set of animals and $B$ represent the set of birds.

Statement A: "Some animals are birds."
This is a standard existential statement (particular affirmative, I-proposition). In set notation, it means there is at least one member in the intersection of animals and birds:
$A\cap B\ne \varnothing$

Statement B: "Some animals are not non-birds."
According to the rule of double negation, a "not non-bird" is simply a "bird". Thus, saying "Some animals are not non-birds" is logically equivalent to saying "Some animals are birds."
In terms of sets, if an animal is not in the complement of $B$ (denoted as $B^{\prime }$), it must be in $B$:
$A\cap {\left(B^{\prime }\right)}^{\prime }\ne \varnothing \Rightarrow A\cap B\ne \varnothing$

Statement C: "Some non-birds are not non-animals."
Applying the double negation rule, a "not non-animal" is an "animal". Therefore, this statement translates to: "Some non-birds are animals" (or "Some animals are not birds").
In set notation, this means:
$B^{\prime }\cap A\ne \varnothing$
This statement asserts the existence of an animal that is not a bird, which is not logically equivalent to Statement A (which asserts the existence of an animal that is a bird).

Statement D: "Some birds are animals."
By the rule of conversion for I-propositions, "Some S is P" is logically equivalent to "Some P is S." Hence, "Some animals are birds" is logically equivalent to "Some birds are animals."
In set notation, since the intersection of two sets is commutative:
$B\cap A\ne \varnothing \iff A\cap B\ne \varnothing$

Comparing these formulations, we find that Statements A, B, and D all represent the same logical relation: the intersection of the set of animals and the set of birds is not empty ($A\cap B\ne \varnothing$). Therefore, statements A, B, and D are logically equivalent.