372-sp08-hwk3-sol-2

# 372-sp08-hwk3-sol-2 - CS 372 Homework 3 Due date: In class...

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CS 372 Homework 3 Due date: In class Thusrday Feb. 28, 2008 By email Sunday 12:59 p.m. to Robert Xiao ( rkx2@cornell.edu ) use subject line (HWK#3 – CS372) SHOW YOUR WORK FOR ALL QUESTIONS 1 Determine the truth value of each of these statements if the domain of each variable consists of all real numbers a) ! x " y (x 2 =y) True (y = x 2 ) b) ! x " y (x = y 2 ) False (if x is negative no such y exists) c) " x ! y (xy = 0) True (x=0) d) " x " y (x + y # y + x) False (communtative law for addition alwyas holds) e) ! x ( x # 0 \$ " y (xy = 1)) True (let y = 1/x) f) " x ! y (y # 0 \$ xy = 1) False (the reciprocal of y depends on y; there is not one x that works for all y) g) ! x " y ( x + y = 1) True (y = 1-x) h) " x " y (x + 2y = 2 % 2x + 4y = 5) False (inconsistent system of equations) i) ! x " y (x+ y = 2 % 2x – y = 1)

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False (this system of equations has only one solution; e.g., if x=0n no y satisfies y =2 and –y = 1) j) ! x ! y " z (z = (x+y)/2) True (z = (x+y) /2) 2 Let F(x,y) be the statement “x can fool y”, where the domains consists of all people in the world. Use quantifiers to express each of these statements: a) Everybody can fool Fred ! (x) F(x Fred) b) Evelyn can fool everybody ! (y) F(Evelyn, y) c) Everybody can fool somebody ! x " y F(x y) d) There is no one who can fool everybody
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## 372-sp08-hwk3-sol-2 - CS 372 Homework 3 Due date: In class...

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