Are there (better) verbs for "and"ing or "or"ing a bunch of clauses together?
Can't believe I didn't think of this earlier... would "conjoin" and "disjoin" work?
'And'ing and 'or'ing are somewhat informal because of how they 'verbify' the conjunctions.
'Conjunction' and disjunction' are the nouns describing such clauses (and note that 'conjunctino' does double duty as the general term for the combining word and also for the 'and'-like word.
That is in some sense formally and logically correct, but making a verb out of these doesn't sound like what you want.
would not come across as 'make the phrase A and B'. It sounds more like 'connect the two' with no implication of it being a boolean function. And 'disjoin' as a verb is even worse (it may not even be a recognized word).
The most accurate forms are:
or less academic sounding:
But informally, your suggested sentences get across the idea very accurately.
As Shyam observed, "and"ing can be described as combining.
A word for the act of "or"ing might be disjunction.
Connect, plain and simple. You connect the clauses using and or or. Which is why they are called logical connectives.
If you're writing about the mathematical or computer operations, I think you're better off to say AND and OR, because your audience should know what those mean. If they don't, they can look them up. If you use some alternative word, your readers are likely to wonder, "Does he mean 'AND'? If he did, why didn't he just say 'AND'?" etc.
If you're looking for a general term that includes AND, OR, and NOT, I'd say "logical operators" or "logical operations". Again, that's the accepted term. As in, "The available logical operators in this language are ..."
If you're talking about common English, if you want to say, "I went to the barbershop AND to the grocery store" but not using the word "AND", that's an entirely different question, and this response is totally irrelevant.