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

The correct answer is "All cats are feline."

To understand why, we need to carefully analyze the original statement and use the rules of classical logic — specifically, the concept of double negation and the relationship between universal affirmative and universal negative statements.

Step 1: Parse the Original Statement

The original statement is: "No cats are non-feline."

This is a universal negative statement of the form "No S are P", where:

- S = cats
- P = non-feline

So it asserts: There does not exist a single cat that is non-feline. In other words, being a cat and being non-feline are mutually exclusive — no member of the set "cats" belongs to the set "non-feline things."

Step 2: Apply the Double Negation Principle

"No S are P" is logically equivalent to "All S are not-P."

This is because saying "No cats are non-feline" means every single cat fails to be non-feline. And if something is not non-feline, then by double negation, it is simply feline.

Formally:
"not non-feline" = "feline"
(A double negation cancels out: ¬(¬feline) = feline)

Step 3: Rewrite the Statement

Substituting this back:

"No cats are non-feline"
⇒ "All cats are not non-feline"
⇒ "All cats are feline"

These three formulations are logically identical — they carry exactly the same meaning and truth conditions.

Step 4: Verify by Elimination of Other Options

Option: "No felines are cats."
This says cats and felines are completely separate groups — the opposite of what the original implies. ✗

Option: "All non-cats are feline."
This makes a claim about non-cats, which goes far beyond what the original statement says. The original only speaks about cats, not about every non-cat in the universe. ✗

Option: "All felines are cats."
This reverses the subject and predicate (the converse). "All cats are feline" does not logically imply "All felines are cats" — there could be felines that aren't cats (e.g., lions or tigers). This is a different, stronger claim. ✗

Conclusion

The statement "No cats are non-feline" directly translates — via the rule that "No S are P" means "All S are not-P," and via double negation — into "All cats are feline." Both statements express the universal truth that every member of the category cat necessarily belongs to the category feline. Therefore, "All cats are feline" is the logically equivalent statement.