hw6fa02 - COT3100.01, Fall 2002 S. Lang (Optional*)...

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COT3100.01, Fall 2002 Assigned: 11/16/2002 (post date) S. Lang (Optional*) Assignment #6 (40 pts.) Due date: 11/26 by 8:45 am in class *This assignment is optional in the following sense: (1) You need to understand the materials contained in this assignment because they provide useful exercises on the last segment of the course; and (2) If you turn in the assignment within the first 15 minutes of the last class (on 11/26), your score on the assignment can be used to replace the lowest score of your earlier assignments (i.e., out of the 6 assignments including this one, the lowest score will be dropped). First, we define some terms and notations. Definition. Consider a binary relation R A × B . The inverse of R , denoted R –1 , is a binary relation B × A such that R –1 = {( b , a ) | ( a , b ) R }, that is, R –1 contains pairs of elements which have the reverse order as they are in relation R . (In some text R –1 is called the converse of R , denoted R c .) Definition. Let R A × A denote a binary relation. The following relations defined over A are called closures : (a) The reflexive closure of R is r ( R ) = R {( a , a ) | a A }. (b) The

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hw6fa02 - COT3100.01, Fall 2002 S. Lang (Optional*)...

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