I'm confirming. If we want to negate something, then parentheses are mandatory.
For example, to make sure this is not Saturday and Sunday, this works:

and not (dayofweek()=6 and dayofweek()=7)

or:

and not (dayofweek()=6) and not (dayofweek()=7)

Screenshots from the expression calculator.

Not working correctly without parentheses :

Working correctly by using parentheses:

Hello dear aigars.kadikis

Let me please do not agree with you. We realized that  functions you mentioned not equal between each other:

and not (dayofweek()=6 and dayofweek()=7)

or:

and not (dayofweek()=6) and not (dayofweek()=7)

Please see test below. Test from today (dayofweek = 1).

This looks really strange. 

Thank you for your support!

It was my mistake to say this will solve the problem:

and not (dayofweek()=6 and dayofweek()=7) 

If we put any two different days in the parentheses, then the outcome will always be true (just like in screenshot). Because it's impossible that "today" can belong to two different week days at the same time. While technical trigger expression does not fail, there is no real-life situation to use it. We should ignore this use case and syntax.

Better to stick to this syntax:

and not (dayofweek()=6) and not (dayofweek()=7)

P.S. Not related to documentation task, but you should use "bigger than" or "less than".

Working days:

dayofweek() < 6

Weekend (Saturday, Sunday):

dayofweek() > 5

The documentation of time functions has been updated in 6.0, 6.4, 7.0 versions to include useful examples from the previous comment by aigars.kadikis.

For a more complex example including "and not", see trigger example 10.