“Only XYZ like ABC” is equivalent to: “Everyone who likes ABC is also an XYZ.”
Since everybody likes at least something, there is no one who likes nothing. The statement: “Everyone who likes nothing is also a man” is true because the “Everyone who likes nothing” part results in 0 people. And it’s true to say that everyone in a group of 0 people is a man. It’s also true that everyone in a group of 0 people is not a man.
But other than vacuous truths, no sentence stating “Only man like XYZ” is true.
Yes there is:
Only men like nothing.
Explanation:
“Only XYZ like ABC” is equivalent to: “Everyone who likes ABC is also an XYZ.”
Since everybody likes at least something, there is no one who likes nothing. The statement: “Everyone who likes nothing is also a man” is true because the “Everyone who likes nothing” part results in 0 people. And it’s true to say that everyone in a group of 0 people is a man. It’s also true that everyone in a group of 0 people is not a man.
But other than vacuous truths, no sentence stating “Only man like XYZ” is true.
But only men like set theory, so…