Home1ReviewQuestions - CS 341 Automata Theory Elaine Rich...

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CS 341 Automata Theory Elaine Rich Homework 1 Due Thursday, September 7 at 11:00 a. m. 1) Write each of the following explicitly: a) P ({ a , b }) – P ({ a , c }) b) { a , b } × {1, 2, 3} × c) { x : ( x 7 x 7} d) { x : 5 y ( y < 10 ( y + 2 = x ))} (where is the set of nonnegative integers) e) { x : 5 y ( 5 z   (( x = y + z ) ( y < 5) ( z < 4)))} 2) Give an example, other than one of the ones in the book, of a relation on the set of people that is reflexive and symmetric but not transitive. 3) Define p to be “equivalent modulo p ”. x p y iff x modulo p = y mod p . For example 4 3 7 and 7 5 12. Let R p be a binary relation on , defined as follows, for any p 1: R p = {( a , b ): a p b } So, for example R 3 contains (0, 0), (6, 9), (1, 4), etc., but does not contain (0, 1), (3, 4), etc. a)
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