Turning logical expression around - c++

Question

I have the following code:
bool s = true;
for (...; ...; ...) {
// code that defines A, B, C, D
// and w, x, y, z
if (!(A < w) && s == true) {
s = false;
}
if (!(B < x) && s == true) {
s = false;
}
if (!(C < y) && s == true) {
s = false;
}
if (!(D < z) && s == true) {
s = false;
}
}
This code is working well. However, I want to, for several (unimportant) reasons, change the code so that I can initiate s = false; and set it to true inside the if-statement. It tried the following:
bool s = false;
for (...; ...; ...) {
// code that defines A, B, C, D
// and w, x, y, z
if (A >= w && s == false) {
s = true;
}
if (B >= x && s == false) {
s = true;
}
if (C >= y && s == false) {
s = true;
}
if (D >= z && s == false) {
s = true;
}
}
However, this is not working properly as the code above is working. I know thought wrong somewhere in the logic, but I can't figure out where. Does anbyone see my probably obvious error?
EDIT: Added three more if-statemets. Missed them since they were commented away.

Answer 1

De Morgan's laws says, you should also change && to || .

Answer 2

!(A < x) is the same as A >= x so your function hasn't reversed the logic at all. You need to use A < x.
I probably wouldn't bother checking the current state of s in the loop. Either you're flipping it or your not. And unless there's some reason to continue through the loop, I'd probably break after flipping s.

Answer 3

I found the answer on Wikipedias page on De Morgan's laws. The correct code for my problem is:
bool s = false;
for (...; ...; ...) {
// code that defines A, B, C, D
// and w, x, y, z
if (!(A >= w || s == false)) {
s = true;
}
if (!(B >= x || s == false)) {
s = true;
}
if (!(C >= y || s == false)) {
s = true;
}
if (!(D >= z || s == false)) {
s = true;
}
}
Thanks #EJP for the tip!

Answer 4

The part of the loop body that sets s is logically equivalent to this:
if(A >= w || B >= x || C >= y || D >= z)
s = false;
Which, abstracting the condition, is equivalent to this:
s &= some_function(A, B, C, D, w, x, y, z);
You want to change it to this:
s |= some_other_function(A, B, C, D, w, x, y, z);
In the first case, s is true after the loop if some_function returns false on every iteration of the loop. In the second true, s is true after the loop if some_other_function returns true on any iteration of the loop.
some_other_function can only ever return true if some_function would return true on any iteration. But some_other_function only has access to the values from the current iteration. Therefore a valid some_other_function cannot exist.
This is assuming s must have the same value after the loop in both cases. Otherwise, you could trivially swap true and false in all the places relating to s.