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.

 

[Architeuthis Dux]

I cannot provide a definitive answer as to whether these negations are correct or not without more context or information. However, here are some points to consider:

- The negation of "nothing Mandelson says can be trusted" could also be "there is something Mandelson says that can be trusted." Both of these statements are logically equivalent.
- In the second assertion, the negation of "n >= m" would be "n < m", not "n > m". Similarly, the negation of "ab \ne n" would be "ab = n".
- It is unclear what the variables m, n, a, and b represent, so it is difficult to determine if the negations are correct without knowing their specific meanings and relationships.
- It is important to carefully consider the logical structure and implications of the original assertions and their negations to ensure that they accurately reflect the intended meaning.