To simplify the problem, one approach is to ignore questions about specific value domains and focus on the logical aspects instead. This can be broken down into different cases such as:
!(A || B) ~= !A && !B
!(A && B) ~= !A || !B
!(!A) ~= A
!(x > y) ~= x <= y
!(x >= y) ~= x < y
The above principles can be extended further for multiple variables like so:
!(A || B || C || D || ...) ~= !A && !B && !C && !D && ...
!(A && B && C && D && ...) ~= !A || !B || !C || !D || ...
Applying these concepts to a specific example, we get:
!((x < 9) && (y <= (8 - x)))
!(x < 9) || !(y <= (8 - x))
(x >= 9) || (y > (8 - x))
Considering additional information that "x and y are whole numbers," a more generalized solution could be expressed as:
(x > 8) || (y > (8 - x))
It's important to assess whether incorporating such details is necessary in each case. While it may lead to a streamlined codebase, it could also result in a less direct relationship with the original wording.