I can understand the and (&&) and or (||) operators, but what's the purpose of the not (!) operator?, C++ FAQ

C++ FAQ / Section 29 / FAQ 29.13

Section 29:

29.1	What is this "newbie section" all about?
29.2	Where do I start? Why do I feel so confused, so stupid?
29.3	Should I use `void main()` or `int main()`?
29.4	Should I use `f(void)` or `f()`?
29.5	What are the criteria for choosing between `short` / `int` / `long` data types?
29.6	What the heck is a `const` variable? Isn't that a contradiction in terms?
29.7	Why would I use a `const` variable / `const` identifier as opposed to `#define`?
29.8	Are you saying that the preprocessor is evil?
29.9	What is the "standard library"? What is included / excluded from it?
29.10	How should I lay out my code? When should I use spaces, tabs, and/or newlines in my code?
29.11	Is it okay if a lot of numbers appear in my code?
29.12	What's the point of the `L`, `U` and `f` suffixes on numeric literals?
29.13	I can understand the and (`&&`) and or (`\|\|`) operators, but what's the purpose of the not (`!`) operator?
29.14	Is `!(a < b)` logically the same as `a >= b`?
29.15	What is this NaN thing?
29.16	Why is floating point so inaccurate? Why doesn't this print 0.43?
29.17	Why doesn't my floating-point comparison work?
29.18	Why is `cos(x) != cos(y)` even though `x == y`? (Or sine or tangent or log or just about any other floating point computation)
29.19	What is the type of an enumeration such as `enum Color`? Is it of type `int`?
29.20	If an enumeration type is distinct from any other type, what good is it? What can you do with it?
29.21	What other "newbie" guides are there for me?

[29.13] I can understand the and (&&) and or (||) operators, but what's the purpose of the not (!) operator?

Some people are confused about the ! operator. For example, they think that !true is the same as false, or that !(a < b) is the same as a >= b, so in both cases the ! operator doesn't seem to add anything.

Answer: The ! operator is useful in boolean expressions, such occur in an if or while statement. For example, let's assume A and B are boolean expressions, perhaps simple method-calls that return a bool. There are all sorts of ways to combine these two expressions:

if ( A &&  B) ...
if (!A &&  B) ...
if ( A && !B) ...
if (!A && !B) ...
if (!( A &&  B)) ...
if (!(!A &&  B)) ...
if (!( A && !B)) ...
if (!(!A && !B)) ...

Along with a similar group formed using the || operator.

Note: boolean algebra can be used to transform each of the &&-versions into an equivalent ||-version, so from a truth-table standpoint there are only 8 logically distinct if statements. However, since readability is so important in software, programmers should consider both the &&-version and the logically equivalent ||-version. For example, programmers should choose between !A && !B and !(A || B) based on which one is more obvious to whoever will be maintaining the code. In that sense there really are 16 different choices.

The point of all this is simple: the ! operator is quite useful in boolean expressions. Sometimes it is used for readability, and sometimes it is used because expressions like !(a < b) actually are not equivalent to a >= b in spite of what your grade school math teacher told you.