Is there a sign for “x's negation equals y”?

Question

For example, let M and N be two real numbers. M is smaller than N. Now I negate the inequality, such that now M is greater or equal to N.

$M < N ≟ M \geq N$

Is there a sign to replace '≟' in the expression above?

Answer 1

It looks like you're talking about equivalence of a proposition to the negation of another. In which case, the "exclusive or" should do:

$$ (M < N) \;\veebar\; (M \geqslant N) $$

asserts that exactly one of the two propositions $M < N$ and $M \geqslant N$ is true. As suggested in the comments (and in Ilya's answer), though, explicitly writing one of

$$\begin{gather*} (M < N) \;\equiv\; \neg (M \geqslant N) \\ (M < N) \;\iff\; \neg (M \geqslant N) \end{gather*}$$

would probably be clearer.

Answer 2

$\quad\quad\Leftrightarrow \neg$