Exercise 5

Simplify the statements below so that negations are only directly next to the predicates.

1. $\neg \exists x \forall y (\neg O(x) \vee E(y))$.
2. $\neg \forall x \neg \forall y \neg(x \lt y \wedge \exists z (x \lt z \vee y \lt z))$.

3. There is a number $n$ for which no other number is either less than or equal to $n$.

4. It is false that for every number $n$ there are two other numbers which $n$ is between.