The correct answer is: after.
The word “after” is used to indicate a time that comes after another time. In this case, the speaker is saying that the person will be discharged after a week. This means that the person will be discharged one week after the current time.
The other options are incorrect because they do not indicate a time that comes after another time. The word “before” is used to indicate a time that comes before another time. The word “from” is used to indicate a starting point in time. The word “since” is used to indicate a time that has passed since a particular event.
Here are some examples of how the word “after” can be used in a sentence:
- I will see you after work.
- The meeting will start after lunch.
- The party will end after midnight.
I hope this helps!