# Negating a statement

State in words the negation of the following sentence: For every martian M, if M is green, then M is tall and ticklish.

I got the right answer to this, give or take a few words, but this is a question of form more than anything. After converting this statement to symbols and negating everything, I come up with: $\exists M(P \wedge (\neg \text{Tall } \vee \neg\text{ Ticklish})$ and so in word format that would be:

There exists a martian such that it is green and not tall or not ticklish.

However the really correct answer is:

There is a martian M such that M is green but M is not tall or M is not ticklish.

The difference between these two is a 'but' and an 'and'. Does this mean anything mathematically? Is my version correct?

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It's the same thing. "$P$ but $Q$" in plain English just means "$P$ and $Q$" with the added connotation that $P$ might suggest $\neg Q$, but nevertheless it is the case that $Q$. –  Rahul Nov 27 '10 at 22:52
How did (number-theory) and (discrete-mathematics) get attached to this? Where is the number theory? Where is the discrete mathematics? Please try to use appropriate tags. This is propositional calculus. –  Arturo Magidin Nov 27 '10 at 23:53

## 1 Answer

Your answer is "really correct". It is perhaps more usual in English to use "but" rather than "and" in a sentence as the one in your example. Formally (i.e., mathematically), there is no difference.

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Oh ok just wanted to make sure, because they mark off points for anything here ;) Thanks –  maq Nov 27 '10 at 23:00