(20 pt., 4 pt. each) Let P(x) be the statement "x is a student," Q(x) be the statement "x is a professor," and R(x,y) be the statement "x asked a question to y." If the domain of x and y consists of all people, express each of the following sentences in terms of P(x), Q(x), R(x,y), quantifiers, and logical operators a. It is not the case that some professor has never been asked a question. b. There is a student who has never asked a question to a professor c. Some student has asked every professor a question. d. There is a professor who has been asked a question by exactly one student. e. There are two different students who have asked each other a