Let's say we have a boolean function to determine if a certain number is acceptable,

Suppose we are now presented with the task of designing a boolean function that determines whether a function is unacceptable.

In Python, we would normally do something like this:

def is_unacceptable(bool_value: bool) -> bool:
    return not is_acceptable(bool_value)

A more generalized approach to this would be:

def negate(boolValue: bool) -> bool{
    return not boolValue
}
def isUnacceptable(boolValue: bool) -> bool {
    return negate(isAcceptable(boolValue));
}

Let's try to define $\text{negate}(x)$ mathematically. What we would like to do here is switch the outputs of the above function, such that we map $0$ to $1$ and $1$ to $0$. That is, we want to design a function $\text{negate}(x)$ such that

One thing to notice is that

So, we can use this to say that

And we're done!