3. (15 pt., 3 pt. each) Let S(x) be the statement "x is a student," P(x) be the statement "x is a professor," and Q(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 S(x), P(x), Q(x, y), quantifiers, and logical operators. Example: Some student has asked every professor a question Answer. 3x(S(x) ^ Vy(P(y) 0(x,y))) Every professor has been asked a question by some student No professor has been asked a question by every student. There is a student who has never asked a question to a professor. There is a professor who has been asked a question by exactly one student There are two different students who have asked each other a question. a. b. c. d. e