Discrete Structures : predicate logic (negations)

Question

Could someone please explain why the negation makes "nobody" into "someone" and not "everyone"

Which of the following is the correct negation for “Nobody is perfect.”

1. Everyone is imperfect. (was my answer)

2. Everyone is perfect.

3. Someone is perfect. (correct answer)

Answer 1

You need to decompose an English sentence into parts that can be manipulated. "Nobody" means "No person".. The negation of "No X is <adjective>" is the statement that says that "No X is <adjective>" is false. And saying that "No X is <adjective>" is false is the same as saying that there is something that makes it false. What would such a thing be? "Some X is <adjective>".

Answer 2

"Everyone is imperfect" has the same meaning as "Nobody is perfect": "For all x, not(perfect(x))." The negation would be "There exists some x such that perfect(x)."

Answer 3

Nobody is perfect. Or equivalently, everyone is imperfect.

The negation: Not everyone is imperfect. Or equivalently, someone is perfect.

General rule: "Someone" is the negation of "nobody".

Answer 4

"Nobody" means "not somebody" and "No one" means "not someone".

So therefore, negation of "Nobody is perfect" is "Somebody is perfect". So therefore, negation of "No one is perfect" is "Someone is perfect".

Note that the negation of "everybody" is "not everybody".