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Inverting Logical Expressions with De Morgan's Laws

A Javascript expression will sometimes be more intuitive (and easier to understand) when written a certain way - but we may actually need the inverse of the expression. For example in listing 1 our code only needs to react if (x && y) is false. We need to invert the expression.
De Morgan's laws describe how to invert a logical expression. In listing 2 let's look at De Morgan's Laws in Javascript syntax.

The rule is to invert each logical term and invert each logical operator.

In listing 3 we invert the expression from listing 1 by applying De Morgan's Laws.
Sometimes a logical term is more complex than a simple boolean variable. A logical term may be a relational expression such as (p < q) from listing 4. We must invert the relational expression as a whole.
Let's invert the expression step by step.

Note that this expression is of the same form as our original expression in listing 1 (x && y) where x is replaced with (p < q) and y is replaced with (r != s). De Morgan's rule is to invert each logical term and invert each logical operator.
Inverting the first logical term (p < q) we get (p >= q)
Inverting the next logical term (r != s) we get (r == s)
Inverting the logical operator && we get ||
Our result is in lst5.
So if you find yourself struggling with a Javascript problem, pick up an old math textbook - your solution is probably in there.