# logical negation of a statement: any mammal that has long ears has at least [closed]

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, ShaktalFeb 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

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"?