Question

logic

2. Schematize, taking the UD to be the class of all persons, and using "P" for "O is a professor", "S" for "O is a student", "R" for "O respects ", and "A" for "O adulates " (10 pts each): a. There is someone who, although not a herself a student, respects any student who respects no professor. b. Every self-respecting student who adulates no professor is respected by some student whom no professor respects.

Answer 1

(a) "There is someone who, although not a herself a student, respects any student who respects no professor." can be rewritten as "There exists an x such that x is not a student and for all y such that y is a student and for all z such that z is a professor, if y does not respect all z, then x respects y"

This is schematized as follows:

3x -S(x) ^ (Vy(S(y) 1Vz(-(R(y, z)))) = R(x, y)))

(b) "Every self-respecting student who adulates no professor is respected by some student whom no professor respects." can be rewritten as "If x is a student such that x repects x and x does not adulate any professor, then there exists a y such that y is a student and all professors do not respect y."

This is schematized as follows:

Val(S(x) R(x,x) ^ Vy(P(y) = -R(z,y))) A R(y,x))] -A(x, y))) = (=y(S(y) ^ Vz(P(z) =