CSC 2510 LAB 3 1. Let P(x) be the statement the word x contains the letter a." What are these truth values? a) Porange) b) Plemon) c) P(true) d) P(false) 2. Translate these statements into English, where R(x) is "x is a rabbit" and H(x) is "x hops" and the domain consists of all animals a) VxR(x) +H(X)) b) Vx(R(x) NI(x)) c) 3x(R(x) +H(*)) d) 3x(R/x) NH() 3. Let Clx,y) mean that student is enrolled in class y, where the domain for * consists of all students in your school and the domain for y consists of all classes being given at your school Express each of these statements by a simple English sentence. a) C(Randy Goldberg, CS 252) b) x(x, Math 695) c) ByC(Carol Sites y d) 3x/C/Math 222)ACO,CS 252)) Baya(cy) (C/A) -C612) va) A (CX) +C) 4. Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives In the domain of all people, let P(x) and F(x) be the statements "x is perfect" and "x is your friend", respectively, a) No one is perfect b) Not everyone is perfect. c) All your friends are perfect. d) At least one of your friends is perfect e) Everyone is your friend and is perfect. + Not everybody is your friend or someone is not perfect. I 5. 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 No one can fool both Fred and Jerry ) Nancy can fool exactly two people. h) There is exactly one person whom everybody can fool 1) No one can fool himself or herself 1) There is someone who can fool exactly one person besides himself or herself 6. Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. a) 3x(x2=2) b) 3x(x=-1) c) Vx(x+221) d) Vx(x #x) 7. First translate into propositional expressions and then use the rules of equivalence and inference to prove the conclusion If the program is efficient, it executes quickly. Either the program is efficient, or it has a bug. However, the program does not execute quickly. Therefore, it has a bug (use letters E, Q.B)