Could you please tell me if I should include "there" and "should" I wrote in parentheses? Thank you.

1) First, Mrs Bennet informs her husband that a rich young bachelor, Mr. Bingley, has just rented the nearby estate of Netherfield and is going to take up residence (there) with some of his servants by the end of the week.
5) He goes on to say that his wife may(should) accompany them because Mr. Bingley may prefer her to their daughters.

Keep there and should; delete may.

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To determine whether to include "there" and "should" in parentheses in these sentences, we need to refer to the original context.

1) First, Mrs Bennet informs her husband that a rich young bachelor, Mr. Bingley, has just rented the nearby estate of Netherfield and is going to take up residence with some of his servants by the end of the week.

In this sentence, the inclusion of "there" in parentheses suggests that the author was contemplating adding additional information about where Mr. Bingley will take up residence. Without more context, it is difficult to determine whether "there" should be included in the sentence.

5) He goes on to say that his wife may accompany them because Mr. Bingley may prefer her to their daughters.

In this case, the inclusion of "should" in parentheses suggests that the author was considering adding a conditional statement, indicating that the wife "should" accompany them. Again, without more context, it is unclear whether the addition of "should" is appropriate in this sentence.

To make a decision about including "there" and "should" in parentheses, you should refer to the original text or consult the author's intention.