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. Эx(S(x) л Vy(РOу) — Q (х, у))) a. Every professor has been asked a question by some student. b. There is a professor who has never been asked a question by any student. c. There is a student who has asked a question to exactly one professor. d. There are two different students who have asked each other a question. 3.
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. Эx(S(x) л Vy(РOу) — Q (х, у))) a. Every professor has been asked a question by some student. b. There is a professor who has never been asked a question by any student. c. There is a student who has asked a question to exactly one professor. d. There are two different students who have asked each other a question. 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3.
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:
ax(S(x) A Vy(P(y)→ Q(x, y)))
a. Every professor has been asked a question by some student.
b. There is a professor who has never been asked a question by any student.
c. There is a student who has asked a question to exactly one professor.
d. There are two different students who have asked each other a question.
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