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.

Is this correct:

1a)NOR(P(u) R(u,v))

1b)NOR(Q(u) R(u,v))

1c)P(u)Q(u) R(u,v)

1D)P(u)Q(u)R(u,v)

1e)P(u)Q(u)R(u,v)R(u,v)

similarily what is nor.
P.S these are probably mistakes?

Explanation / Answer

Given statements are

p(u) - u is a statement
Q(u) - u is a professor

R(u,v) u asked a question to v.

u and v consists of all people

Nor is negative quantifier it was indicated like for example all good its negation is all are not good it was indicated by negation.

So our first question is

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

negation of (there exist p(u) R(u,v))

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

negation of (there exist Q(u) R(v,u))

3a)some student has asked every professor a question

there exist p(u) for all Q(u) R(u,v)

4ans:there is student who has asked a question exactly one professor.

there exist p(u) -> there existQ(u) R(u,v)

5There are two different student who have asked questions each other.

there exist P(u) R(u,v)<->r(u,v)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.