Let () be the statement is a student, () be the statement is a professor, and (, ) be the statement asked a question to . If the domain of and consists of all people, express each of the following sentences in terms of (), (), (, ), quantifiers, and logical operators.

Example: Some student has asked every professor a question.

Answer: (() (() (, )))

1. Every student has asked some professor a question.

2. There is a professor who has never been asked a question by a student.

3. There is a student who has asked a question to exactly one professor.

4. There is a professor who has asked every other professor a question.

5. There are two different students who have asked each other a question.