# Converting Predicate Logic Statement to Negation in English

I'm working on some Predicate Logic and want to express a proposition in English into the negation.

The statement is: "Everyone who has not read a book is dumb"

My question is: Is the negation of this statement - "Some people who have read a book are dumb" or "Some people who have not read a book are dumb" or "Some people who have read a book are not dumb (i.e smart)"?

Would appreciate any explanation. Thanks

It is neither of those three. It is that there are some people who have not read a book but (and) who are not dumb.

In general, the negation of a statement like ‘All of these are like that’ is ‘there are some of these that are not like that.

Here, the these are the things about which you are saying something (the ‘subject term’), while the that is what you say about the these.

For example, the negation of ‘All crows are black’ would be that ‘some crows are not black’. (these are crows; that is being black)

In your case, the these are people who have not read a book, while the that is being dumb.

So, with the ‘Some of these are not that, you get the answer I provided above.

Finally, please don’t use ‘smart’ as the negation of dumb… someone can be neither dumb nor smart.

• So to check my understanding, the statement "Everyone who has not been fed got sick" would be "Some people who have not been fed have not got sick"? Commented Nov 13, 2021 at 17:50
• @LiteralJumpingAddition Exactly right! Commented Nov 13, 2021 at 18:13