P(u) be the statement \"u is a student,\" Q(u) be the statement \"u is a profess

Question

P(u) be the statement "u is a student," Q(u) be the statement "u is a professor," and R(u,v) be the statement "u asked a question to v". If the domain of u and v consists of all people, express each of the following sentences in terms of P(u), Q(u), R(u,v), quantifiers, and logical operators.
1a) It is not the case that some student has never asked a question.
1b) There is a professor who has never been asked a question by a student.
1c) Some student has asked every professor a question.
1d) There is a student who has asked a question to exactly one professor.
1e.) There are two different studnets who have asked each other a question.

What?!?! Please explain.

Explanation / Answer

1a)It is not the case that some student has never asked a question.

¬(P(u) R(u,v))

1b)There is a professor who has never been asked a question by a student

¬(Q(u) R(u,v))

1c)Some student has asked every professor a question.

P(u)Q(u) R(u,v)

1D)There is a student who has asked a question to exactly one professor.

P(u)Q(u)R(u,v)

1e)There are two different studnets who have asked each other a question.

P(u)Q(u)R(u,v)R(u,v)

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