please help 1- Let () be the statement “ is a student,” () be the statement “ is
ID: 3746635 • Letter: P
Question
please help
1- Let () be the statement “ is a student,” () be the statement “ is a professor,” and (, ) be the statement “ asked a question to .” If the domain of and consists of all people, express each of the following sentences in terms of (), (), (, ), quantifiers, and logical operators.
Example: Some student has asked every professor a question.Answer:
(() (() (, )))
a- Every student has asked some professor a question.
b- There is a professor who has never been asked a question by a student.
c- There is a student who has asked a question to exactly one professor.
d- There is a professor who has asked every other professor a question.
e- There are two different students who have asked each other a question.
Explanation / Answer
a- Every student has asked some professor a question.
(() (() (, )))
b- There is a professor who has never been asked a question by a student.
(() (() (, ))) evaluates to {<null>} i.e. subject to y = 0.
c- There is a student who has asked a question to exactly one professor.
(() (() (, ))) i.e. subject to x = 1, y = 1.
d- There is a professor who has asked every other professor a question.
z(P(z) (() (z, )))
e- There are two different students who have asked each other a question.
((() (S() (, )))) (y((y) x(S(x) (y, x))))
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