In many contexts, the meanings are pretty much the same, but you might hear finished more often than completed in casual conversation. For example:
I've finished my shopping.
She finished the song.
He finished the race.
I could use completed in those sentences – the meaning wouldn't change, but the register might sound off.
The word completed can convey some sense of accomplishment. In the context of a race, it might work when the race is a major achievement:
He completed his first marathon last year.
Homework, though, is not really a major achievement, so I think you'd hear finished more often in casual conversation:
“Joey, where are you going? Did you finish your homework?”
That said, you might see completed in more formal contexts, such as a paper on education, or a course syllabus:
Students must complete six homework assignments during the semester.
When you disapprove of someone or something, you simply have a negative opinion of it:
My mother disapproves of the woman I am seeing.
When you disapprove something, you reject something, usually having the official power to do so:
The principal disapproved the students' request for less homework.
Based on this second definition, it is less likely that you would disapprove people, rather than things. But you might:
The mayor disapproved the new nominee for dogcatcher.
Conversely, if you added of, the mayor would just be offering a personal opinion, not officially rejecting the nominee:
The mayor disapproved of the new nominee for dogcatcher.
Best Answer
There isn't much of a difference here. In sentence B you're using the sentence structure
{Do something} for {Reason}. Examples include:
Sentence A uses a specific kind of English idiomatic phrase {Go somewhere} on {type of time}. By 'type of time' I usually mean something like "business" or "vacation". Examples include:
but not
If you're ever unsure whether to use "on" or "for" in that type of sentence, "for" almost always works, and "on" is only correct for a specific few cases. For example, you could say "Go to New Zealand for February" and that would mean you were spending the entire month in New Zealand.