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Recursive theorm

Posted on 2011-10-20
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Let K be the set of all cities that you can get to from Toronto by taking flights (or sequences of flights) on commercial airlines. Give a recursive definition of K.

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Question by:mustish1

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Accepted Solution

This is a recursive definition for a set Z of ordered pairs:

B. (2,4) is in Z.
R1. If(x,y) is in Z with x < 10 and y <10, then (x+1, y+1) is in Z.
R2. If(x,y) is in Z with x > 1 and y < 10, then(x-1, y+1) is in Z.

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This is a recursive definition for a set K of cities:

B.    Toronto is in K.
R1.  If there is ......  for city_k,  then city_k is in K.
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