expr is the logical NOT function. It gives False if expr is True, and True if it is False.
] can be input in StandardForm and InputForm as ¬expr. The character ¬ can be entered as !, not or \[Not].
Not gives symbolic results when necessary, and applies various simplification rules to them.
If you are using Mathematica with a text-based front end, then you cannot use the notation !
expr for Not[
] if it appears at the very beginning of a line. In this case, !
expr is interpreted as a shell escape.