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javascriptlogic

How to rewrite a negated line?

Negating takes me hours of trial and error until nothing breaks, any method of negating other than intuitively? For example:

//x and y are whole numbers

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

  • The simplest thing is to ignore questions about the domain of values, and treat this as an entirely logical problem. Then we can break it down into cases such as:

    !(A || B) ~= !A && !B
!(A && B) ~= !A || !B
!(!A) ~= A
!(x > y) ~= x <= y
!(x >= y) ~= x < y

    The first two can easily be extended:

    !(A || B || C || D || ...) ~= !A && !B && !C && !D && ...
!(A && B && C && D && ...) ~= !A || !B || !C || !D || ...

    So, for one of your examples, we have:

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

    We could leave it as this, but as you had additional domain information, ("x and y are whole numbers"), you might incorporate it to return a slightly less specific, but accurate enough in context answer, such as

    (x > 8) || (y > (8 - x))

    You would have to decide on a case-by-case basis whether this is worth the additional steps. What it might gain is a somewhat reduced codebase, it can also lose in a less transparent link to the original format.