please help

1- 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:

(() (() (, )))

a- Every student has asked some professor a question.

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

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

d- There is a professor who has asked every other professor a question.

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