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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.

S Hristoskov
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  • Your last statement: Do you mean that instead of "not all redheaded persons....", you need to exchange it with "exists a redheaded person (who fails to satisfy the rest of the statement? That's simply a matter of equivalence. "not all x satisfy P(x)" is equivalent to "exists x such that it isn't the case that P(x). – amWhy Apr 23 '17 at 20:43
  • I won't assist you on any more questions you post, SHristoskov, until you include in your posts, your own attempts to address the question you intend to post here. There isn't even a proper question asked in your post! "I want (you guys) to negate the following sentence:" "I must not negate the quantifier" i.e.(you guys provide a negation that doesn't start with "not all ..."). In turn, I want that askers take time, apply effort and to make an attempt, or two, or three!, before asking questions here. – amWhy Apr 23 '17 at 20:57
  • Possible duplicate of Negating a quantified formula –  Apr 23 '17 at 21:03

1 Answers1

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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.

awright96
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  • No, The outermost quantifier ($\forall$) is a strong signal that the main connective for the sentence is implication. All redheaded persons in the room have a pet that is either a cat or dog" translates to "For all persons $a$ (If ($a$ is a redhead and is in the room), then ($a$ has a pet and this pet is either a cat or a dog.))" – amWhy Apr 23 '17 at 20:26
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    But I think your natural language version of its negation is just fine, awright96. – amWhy Apr 23 '17 at 20:30
  • I think your interpretation is equally as valid as my own, but 'There exists a redheaded person in the room who has no pet or has a pet which is not a cat or dog' is still a valid negation of your interpretation. – awright96 Apr 23 '17 at 20:32
  • Precisely; that's a phenomenon that's bound to occur when trying to represent logic using natural language, and the other way around! – amWhy Apr 23 '17 at 20:33
  • I just countered the downvote you received, awright96. It's too bad the downvoter never expressed why s/he downvoted your post. – amWhy Apr 23 '17 at 21:00