Chapter 1 - Section 1.5 - Nested Quantifiers - Exercises - Page 66: 15

a) VxN(x, discrete mathematics), where N(x, y) is "x needs a course in y" and the domain for x is computer science students and the domain for y is academic subjects b) 3xO(x,personal computer), where O(x,y) is "x owns y," and the domain for xis students in this class c) Vx3yP(x,y), where P(x,y) is "x has taken y"; x ranges over students in this class, and y ranges over computer science courses d) 3x3yP(x, y), with the environment of part (c) (i.e., the same definition of P and the same domain) e) VxVyP(x,y), where P(x,y) is "x has been in y"; x ranges over students in this class, and y ranges over buildings on campus f) 3x3yVz(P(z,y)--+ Q(x,z)), where P(z,y) is ''z is in y" and Q(x,z) is "x has been in z"; x ranges over students in this class, y ranges over buildings on campus, and z ranges over rooms g) VxVy3z(P(z, y) /\ Q(x, z)), with the environment of part (f)

a) VxN(x, discrete mathematics), where N(x, y) is "x needs a course in y" and the domain for x is computer science students and the domain for y is academic subjects b) 3xO(x,personal computer), where O(x,y) is "x owns y," and the domain for xis students in this class c) Vx3yP(x,y), where P(x,y) is "x has taken y"; x ranges over students in this class, and y ranges over computer science courses d) 3x3yP(x, y), with the environment of part (c) (i.e., the same definition of P and the same domain) e) VxVyP(x,y), where P(x,y) is "x has been in y"; x ranges over students in this class, and y ranges over buildings on campus f) 3x3yVz(P(z,y)--+ Q(x,z)), where P(z,y) is ''z is in y" and Q(x,z) is "x has been in z"; x ranges over students in this class, y ranges over buildings on campus, and z ranges over rooms g) VxVy3z(P(z, y) /\ Q(x, z)), with the environment of part (f)