C++ Syntax – Are ‘not, and, or, not_eq’ Part of the Standard?

They are in fact standard in C++, as defined by the ISO 14882:2003 C++ standard 2.5/2 (and, indeed, as defined by the 1998 edition of the standard). Note that they are built into the language itself and don't require that you include a header file of some sort.

However, they are very rarely used, and I have yet to see production code that actually uses the alternative tokens. The only reason why the alternative tokens exist in the first place is because these characters on some keyboards (especially non-QWERTY ones) were either nonexistent or clumsy to type. It's still in the standard for backwards compatibility.

Even though they are standard, I highly recommend that you don't use them. The alternative tokens require more characters to type, and the QWERTY keyboard layout already has all the characters needed to type out C++ code without having to use the alternative tokens. Also, they would most likely bewilder readers of your code.

2.5/2 Alternative tokens

In all respects of the language, each alternative token behaves the same, respectively, as its primary token, except for its spelling. The set of alternative tokens is defined in Table 2.

Table 2 - alternative tokens
+--------------+-----------+
| Alternative  |  Primary  |
+--------------+-----------+
|    <%        |    {      |
|    %>        |    }      |
|    <:        |    [      |
|    :>        |    ]      |
|    %:        |    #      |
|    %:%:      |    ##     |
|    and       |    &&     |
|    bitor     |    |      |
|    or        |    ||     |
|    xor       |    ^      |
|    compl     |    ~      |
|    bitand    |    &      |
|    and_eq    |    &=     |
|    or_eq     |    |=     |
|    xor_eq    |    ^=     |
|    not       |    !      |
|    not_eq    |    !=     |
+--------------+-----------+