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Write the negation of the following statement: Any mammal that has long ears has at least one of its predators with yellow eyes having all of its cubs that cannot fly. Write it in the logical mathematical way.

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closed as off-topic by Rahul, user127.0.0.1, Sami Ben Romdhane, Lost1, Shaktal Feb 18 '14 at 21:50

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It just takes unpacking. Remember to flip the for all and there exists and to negate the inside. Where are you having trouble? – Ross Millikan Feb 18 '14 at 21:20
My only trouble is just expressing the statement as it is given, because after that i can easily negate it..@RossMillikan – user123 Feb 18 '14 at 21:24
Are you trying to write it in English, or in some logical language? If the latter, you need to define what language. – Ross Millikan Feb 18 '14 at 21:25
yes you are right...i need to write it in logical language @RossMillikan – user123 Feb 18 '14 at 21:30
up vote 2 down vote accepted

The simple way is to define $P$ as "any mammal that has long ears has at least one of its predators with yellow eyes having all of its cubs that cannot fly" and the negation is $\lnot P$. Presumably you are supposed to define simpler sentences than that, so $M(x)$ is $x$ is a mammal,$ L(x)$ means $x$ has long ears, and your sentence looks like $\forall x (M(x)\wedge L(x))\implies \dots$ Can you finish?

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i don't really know how to use the latex guide of this page for this logic statement...but i am expressing it with words and after that i hope you correct me.. Let there exist one N(x) such that x is a predator and it has P(x) yellow eyes and let Q(x) the cubes that can fly and this be in negation form..? – user123 Feb 18 '14 at 21:40
You can see this for $\LaTeX$ and right click and Show Math as -> TeX commands to see how I did anything in any post. That's how I learned. – Ross Millikan Feb 18 '14 at 21:42
Can you please help me clearly express this one?? @RossMillikan – user123 Feb 18 '14 at 21:51
The next part of the sentence, "has at least one" would translate to "there exists..." Can you make progress from here? – Ross Millikan Feb 19 '14 at 17:17
yes i have written it with words in the comment above, i am just having problem with the paranthesis.. – user123 Feb 19 '14 at 17:19

What about this (in a bit free literary form): "All yellow eyes predators of some long ears mammals have flying cubs"?

Vladimir Sotirov

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No, that doesn't really work: "of some long-eared mammals" is not well-defined, at least to this native English speaker. – TonyK Feb 18 '14 at 21:45
Thank you, Tony, that is what I wanted to say in bad English. I think we are wright to say in our case "All A of some B are..." instead of "There are such B that for all A..."? – Vladimir Sotirov Feb 18 '14 at 22:06
No, I disagree. The English language simply doesn't assign a precise meaning to "all A of some B". – TonyK Feb 18 '14 at 22:12
Sure! Of course, we have in mind one and the same predicate formula, but I am trying to translate it in an everyday language more appropriate for a puzzle (passing from Bulgarian to English :)) If we are asked the question "Are there any animals all of whose enemies are flying?" the logically exact answer will be "Yes, there are such animals all of whose enemies..." But I suppose that something like "Oh, yes, all enemies of some reptiles, for instance, are flying" with the natural emphasizing would be relevant, too. I'm sorry, this is rather linguistic matter indeed. – Vladimir Sotirov Feb 18 '14 at 22:58

"There is a long-eared mammal, all of whose yellow-eyed predators have flying cubs."

(By the way, cubs never fly. Better is "flying young".)

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