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### MJPS6

Course: HRS 312, Fall 2009
School: Creighton
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Word Count: 382

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303: HRS Gdel, Escher, and Bach (Spring 2007) Problem Set 6: TNT and Quantifiers 6.1 Which of the following correctly pair a statement of number theory with a more elemental interpretation? Statement of number theory a. 7 is not prime Elemental interpretation There exists numbers c and d, both greater than 1, such that c times d equals 7. b. A number is always less For every number b, that number b is less than...

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303: HRS Gdel, Escher, and Bach (Spring 2007) Problem Set 6: TNT and Quantifiers 6.1 Which of the following correctly pair a statement of number theory with a more elemental interpretation? Statement of number theory a. 7 is not prime Elemental interpretation There exists numbers c and d, both greater than 1, such that c times d equals 7. b. A number is always less For every number b, that number b is less than its square than b times b. c. All multiples of 4 are also For every number b such that there exists multiples of 2 a number c where 4 times c equals b, there also exists a number d where 2 times d equals b. 6.2 Provide elemental interpretations of the following statements of number theory: a) 1363 is a multiple of 47 b) No number is simultaneously even and odd c) There are an infinite number of even numbers d) Three times any number is always greater than two times any number 6.3 Interpret the following statements in simple English: a) There is no number c such that c times c equals 47 b) There exists a number a such that there are no b numbers and c, both greater than 1, where b times c equals a and there are no numbers d and e, both greater than 1, where d times e equals a plus 2 6.4 Translate each statement below into English and determine whether or not it is true: a) c: (c+S0) = SS0 b) c: (c+S0) = SS0 c) a: b: c: (a = ((b b) b) + ((c c) c)) 6.5 Identify the free variable(s) and quantified variables in the examples of open and closed statements in English given below. Be sure to distinguish the open sentences from the closed sentences. a) (x) y loves x. b) (x)(y) if y loves x then x loves y. c) (x)( y) x loves y and y loves x. 6.6 For each of the...

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