Question: how to write a negation in math?
Answer: Negation of "If A, then B". Consider the statement "If I am rich, then I am happy." For this statement to be false, I would need to be rich and not happy. If A is the statement "I am rich" and B is the statement "I am happy,", then the negation of "A $\Rightarrow$ B" is "I am rich" = A, and "I am not happy" = not B.