# 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?

• 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 $Q$.
– user856
Nov 27, 2010 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. Nov 27, 2010 at 23:53