Rubinstein2005-page57

Rubinstein2005-page57 - October 21, 2005 12:18 master Sheet...

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Unformatted text preview: October 21, 2005 12:18 master Sheet number 55 Page number 39 Choice 39 Let X be a finite grand set. A list is a nonempty finite vector of elements in X . In this problem, consider a choice function C to be a function that assigns to each vector L = < a 1 , . . . , a K > a single element from { a 1 , . . . , a K } . (Thus, for example, the list < a , b > is distinct from < a , a , b > and < b , a > ). For all L 1 , . . . , L m define < L 1 , . . . , L m > to be the list that is the concatena- tion of the m lists. (Note that if the length of L i is k i , the length of the concatenation is 6 i = 1, ... , m k i ). We say that L extends the list L if there is a list M such that L = < L , M > . We say that a choice function C satisfies property I if for all L 1 , . . . , L m C (< L 1 , . . . , L m >) = C (< C ( L 1 ) , . . . , C ( L m ) >) . a. Interpret property I . Give two (distinct) examples of choice functions that satisfy I and two examples of choice functions which do not....
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