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Solve the following problems and submit them in class by December 1, 2009:

Problem 1 With , and as below, write as a composition of and two 's, using he basic TG operations , , and .


Problem 2 Show that the "topological boundary" operator and the "crossing change" operator of the class of November 5 are compositions of the basic TG operations , , and (you are also allowed to use "nullary" operations, otherwise known as "constants").

Problem 3 Write the third Reidemeister move R3 as a relation on .