Can any kind soul please explain why
! (x < 0 && y < 0)
is not equivalent to the following two expressions
!(x < 0) && ! (y < 0) AND x > 0 && y > 0
In the first code doesn't it imply that, x is not less than 0 and y is not less than 0? and does it also not mean that x and y should be more than 0? Any help is much appreciated!
In your two rewritten versions, you'd need OR (||) rather than AND (&&). This is true any time you invert an AND condition's component parts.
! (x < 0 && y < 0) is true if x is >= 0 and y is < 0. To get that same result in the other form, you'd need x >= 0 || y >= 0. (Note that it's >=, not just >, but the main point was the || rather than &&.)
As ernest_k points out, this is one specific application of De Morgan's laws.
Let's calculate the equivalent expression for ! (x < 0 && y < 0)
Note that if negation comes before &&, it becomes || and vice versa. so your expression would be equal to :
! (x < 0 && y < 0) ---> !(x<0) || !(y<0) ---> x>=0 || y>=0
it's like the figure bellow, colored area is the result of your expression :
In the first example both of the expressions in brackets ("(x < 0)" and "(y < 0)") have to be equal to "true" for the whole expression to become "false".
In the second example the first two expressions contain each one of the expressions, which are inside the brackets of the first example ("(x < 0)" and "(y < 0)"). So only one of these expressions being "true", can cause the whole expression to become "false" since everything is connected with AND operators.
You can set x=0 and y=-1 and try it out manually.
You also might be interested in having a look at https://en.wikipedia.org/wiki/De_Morgan's_laws
x > 0 && y > 0should use>=, not just>.