Let P (x) be the statement "x can speak Russian" and let Q(x) be the statement "x knows the computer language C++." Express each of these sentences in terms of P (x), Q(x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school. a) It is not the case that all students at your school can speak Russian and who knows C++. b) There is a student at your school who cannot speak Russian but who knows C++. c) Every student at your school cannot speak Russian or does know C++. d) No student at your school can speak Russian or knows C++. Let F(x, y) be the statement "x can fool y," where the domain consists of all people in the world. Use quantifiers to express each of these statements. a) Everybody can fool Fred. b) Evelyn can fool everybody. c) Everybody can fool somebody. d) There is no one who can fool everybody. e) Everyone can be fooled by somebody. f) No one can fool both Fred and Jerry.

5. Let P (x) be the statement “x can speak Russian” and let Q(x) be the statement “x knows the computer language C++.” Express each of these sentences in terms of P (x), Q(x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school. a) It is not the case that all students at your school can speak Russian and who knows C++. b) There is a student at your school who cannot speak Russian but who knows C++. c) Every student at your school cannot speak Russian or does know C++. d) No student at your school can speak Russian or knows C++. 6. Let F(x, y) be the statement “x can fool y,” where the domain consists of all people in the world. Use quantifiers to express each of these statements. a) Everybody can fool Fred. b) Evelyn can fool everybody. c) Everybody can fool somebody. d) There is no one who can fool everybody. e) Everyone can be fooled by somebody. f) No one can fool both Fred and Jerry.