ALGEBRA PROPERTIES PROJECT TABLE: CARD ROTATIONS AND FLIPS

Project http://www.jug.net/wt/algpropc.htm by William V. Thayer

NAME _________________________________ DATE _____/_____/_____

The operation is: ROW ELEMENT "FOLLOWED BY" COLUMN ELEMENT in the table.   Example:     m • R = V

• Operation Table
  •     I     R     T     L     H     m     V     d  
 I                 
 R                 
 T                 
 L                 
 H                 
 m      V             
 V                 
 d                 

Some basic algebra properties ( such as CLOSURE, ASSOCIATIVE, IDENTITY and INVERSE) seem to be true for the "followed by", • operation. Can you show that the COMMUTATIVE property does not hold for all the combinations of two elements in the table above. State an example from the table that proves the COMMUTATIVE property fails to hold. This method of proof is called a proof by COUNTER EXAMPLE. (3 points if you show how)


How would you prove that one of the other properties holds for the table? (2 points if you show how) Bring your comments to class for a discussion.



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