What is the best way to rephrase a sentence that contains a double negative

Figuring out how to negate a condition often requires hours of trial and error to avoid breaking anything. Is there any method for negating conditions other than relying on intuition? For instance:

//x and y are whole numbers

!((x<9) && (y<=(8-x)))
((x>8) || (y>(8-x)))

Answer №1

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.

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