Which of the following statements is logically equivalent to the statement “No cats are non-feline.”?

The correct option is All cats are feline.

To understand why these two statements are logically equivalent, we can analyze the relationship between the categories using set theory and translation of categorical propositions.

Let us define the terms involved:
Let C represent the set of all cats.
Let F represent the set of all felines.
Therefore, "non-feline" refers to the complement of the set of felines, which we can write as F'.

The original statement is: "No cats are non-feline."
This categorical proposition asserts that there is no overlap between the set of cats (C) and the set of non-felines (F'). In set theory notation, this is expressed as the intersection of the two sets being empty:

$C\cap F^{\prime }=\varnothing$

If there are no cats that lie outside the set of felines, it logically follows that every cat must be inside the set of felines. In set theory, this relationship is expressed as a subset:

$C\subseteq F$

Translating the subset relation $C\subseteq F$ back into standard English gives us: "All cats are feline."

Therefore, the statement "No cats are non-feline." is logically equivalent to "All cats are feline."