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?