Negating a quantified formula NOR

Question

I want to negate the following sentence:

All redheaded persons in the room have a pet , that either cat or dog is 

I must not negate the quantifier.

Answer 1

The negation of this sentence can be kind of nuanced, especially for a nonnative English speaker (which I assume you are because of the misplaced verb in the question). I'm assuming you want the negation of the sentence,

All redheaded persons in the room have a pet that is either a cat or a dog.

This is kind of tricky because there is an implied 'and' in the sentence. With the 'and' included, it should be,

All redheaded persons in the room have a pet AND that pet is either a cat or a dog.

So the negation of this sentence would be,

There exists a redheaded person in the room who has no pet or has a pet which is not a cat or dog.