How to Negate Complex Logical Assertions in Mathematics?

[Pythagorean12]

Homework Statement

Write down the negations of the following assertions (where m, n, a, b are natural numbers):

a) if Coke is not worse than Pepsi then nothing Mandelson says can be trusted.
b) $$\forall m \exists n\forall a\forall b (n >= m)$$ /\ $$[(a=1)$$ \/$$(b=1)$$ \/ $$(ab \ne n)]$$

Answers:
a) if Coke is not worse than Pepsi then everything Mandelson says can be trusted.
b) $$\exists m\forall n \exists a\exists b (n < m)$$ \/$$[(a \ne 1)$$ /\ $$(b \ne 1)$$ /\ $$(ab =n)]$$

Could anyone check whenever or not these answers are correct?

 

[HallsofIvy]

Since you have not said what "a", "b", "m", or "n" mean, it is impossible to tell.

I will say this- the negation of an "if- then" implication is NOT an "if-then" implication.