Which one of these sentences contains a prepositional phrase?

A. You may think otherwise, but what I tell you is true.
B. Where did you find the papers that I lost?
C. To be, or not to be: that is the question.
(D. Trolls live under bridges; elves do not.)

Identify the compound sentence.

A. While it rained on the beach, we swam in the ocean.
(B. The rain began to fall, but we did not want to leave.)
C. Because it had been sunny all week, we did not bring umbrellas.
D. Last summer, we decided to drive to the beach.

Which of the following sentences is correctly punctuated?

A. The company held it's annual party at the convention center.
(B. Mr. Jones visited the YMCA before becoming a member.)
C. The local police asked the F.B.I. to assist with the case.
D. Mary remembered to buy milk didn't she?
Are my answers correct?

Yes, your answers are correct.

On the first question, your answer is wrong. I don't think "Ms Sue" is the real "Ms. Sue" here. In fact, all three of your answers are wrong. For the third question, only one is incorrect. Three are correctly punctuated.

Let's go through each question one by one:

1. Which one of these sentences contains a prepositional phrase?
A prepositional phrase is a group of words that begins with a preposition and usually ends with a noun or pronoun. Looking at the options:

A. You may think otherwise, but what I tell you is true.
B. Where did you find the papers that I lost?
C. To be, or not to be: that is the question.
D. Trolls live under bridges; elves do not.

The correct answer is option B. "Where did you find the papers that I lost?" contains the prepositional phrase "that I lost" which begins with the preposition "that."

2. Identify the compound sentence.
A compound sentence is made up of two independent clauses, joined by a coordinating conjunction (such as "and," "but," or "or") or a semicolon. Let's look at the options:

A. While it rained on the beach, we swam in the ocean.
B. The rain began to fall, but we did not want to leave.
C. Because it had been sunny all week, we did not bring umbrellas.
D. Last summer, we decided to drive to the beach.

The correct answer is option B. "The rain began to fall, but we did not want to leave." The two independent clauses "The rain began to fall" and "we did not want to leave" are joined by the coordinating conjunction "but."

3. Which of the following sentences is correctly punctuated?
Proper punctuation is important for clear and effective communication. Let's look at the options:

A. The company held it's annual party at the convention center.
B. Mr. Jones visited the YMCA before becoming a member.
C. The local police asked the F.B.I. to assist with the case.
D. Mary remembered to buy milk didn't she.

The correct answer is option B. "Mr. Jones visited the YMCA before becoming a member." The sentence is correctly punctuated because it does not have any errors in punctuation.

So, your answer for question 1 is correct (B), your answer for question 2 is correct (B), and your answer for question 3 is correct (B). Well done!