What is the meaning of the prefix verab in the german word Verabredung? I assume it is a combination of ver and ab, but in this case, what does it express semantically?
normally German ab is the equivalent of English off and expresses 'separation', but here it is indeed hard to understand how agreeing on an appointment is linked to the concept of separation.
Since Verabredung is a noun derived from the verb verabreden, let's look at verbs that begin with verab-. The first thing to note is that the group is very small. The pattern is not productive (in the linguistic sense; see Wikipedia). There are no new verbs being formed with verab-.
verabreden, verabreichen, verabscheuen, verabschieden
Interestingly, the nouns Abschied and Abscheu (with the appropriate meaning) exist, so these verbs could be analyzed as adding ver- to a nominal base. But this doesn't work for verabreichen, as there is no potential base starting with Abreich-. It hardly works for verabreden either, as Abrede is quite restricted in the way it can be used (it mostly occurs as in Abrede stellen).
Either way, these verbs behave just like verbs with the prefix ver-:1
They can occur in fronted position:
Ich verGESse nie etwas. Wir verABreden uns zum Training.
Zu precedes the verb:
ohne es zu verGESsen, ohne sich zu verABschieden
There is no ge- in the past participle:
Hast du es verGESsen? Hast du dich verABschiedet?
Could they be analyzed as ver- plus a verbal base? They could, with an important caveat: The putative verbal bases must then be analyzed as cranberry morphemes (Wikipedia) that do not exist on their own. (Three of them – abreichen, abscheuen, abschieden – do not exist at all, and for abreden, the meaning doesn't fit very well.) This can be compared to a verb such as verlieren: lieren does not exist on its own, either.2
It follows from all of the above that the meaning of these verbs can't be derived from the meaning of the parts. In fact, it seems best to not see them as derived at all. Although ver- can be seen as indicating transitivity at least.
1 Should verAB- be analyzed as a prefix as the question suggests? I think not: verb prefixes don't bear stress, only verbal particles do. And those behave differently than prefixes: Komm zuRÜCK! zuRÜCKgekommen, zurRÜCKzukommen.
2 But note that deriving e.g. verabreden from ver- plus abreden is unusual, as abreden is made up of two words: a verbal particle and a verb.
Die Verabredung is a noun made from the verb verabreden.
The verb verabreden means to agree. You can boil it down to
reden – to talk
abreden, absprechen – to bargain, to negotiate
So, abreden and absprechen is alternating in talk. You may draw a line to abgeben which means to pass, and abfallen which means to come loose. The prefix ab- often means something got loose.
verabreden – to agree
So, verabreden is coming to a conclusion in abreden. Conclusion is a function ver- often carries.
In addition, there are multiple ways to make a noun from a verb:
der/die/das Verabredende (from Partizip I) — the person who makes an agreement
das Verabredete (from Partizip II) — the thing agreed upon
das Verabreden (from Infinitiv) — the action of making an agreement
die Verabredung (from Infinitiv) — the agreement