I am giving the following statements and I have to formalize them into mathematical notation. Moreover I have to negate them. It would be amazing if you could be my second pair of eyes to proofread my answers!
(1) Every Element of $M$ is negative
My response: $\forall m \in M : m<0$ with the negation $\exists m \in M : m\geq 0$
(2) Between two different elements of $M$ there is another element of $M$.
My response: $\forall m,n\in M:m \neq n$ $\exists z\in M: m<z<n \vee m>z>n$ with the negation $\forall z \in M : m=z=n$ $\exists m,n \in M: m=n$.
(3) $M$ contains at least two elements
My response: $\exists m_1,m_2\in M : m_1\neq m_2$ with the negation $\forall m_1,m_2\in M : m_1=m_2$.
(4) Every element of $M$ can be expressed as the product of two different elements of $M$.
My response: $\forall m\in M$ $\exists m_1,m_2 \in M: m_1 \neq m_2 \land m_1\cdot m_2=m$ with the negation $\forall m_1,m_2 \in M : m_1=m_2$ $\exists m\in M: m_1\cdot m_2\neq m$