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Unformatted text preview: MATH 74 HOMEWORK 2 (DUE WEDNESDAY SEPTEMBER 19) 14. In each of the following problems I give you a binary operation on a set. (You can check or take for granted that it does indeed make sense; I’m not going to play games by giving you a formula that doesn’t actually define a binary operation.) I want you to (a) Prove that the binary operation is commutative, or exhibit an explicit coun terexample showing that it is not. (b) Prove that the binary operation is associative, or exhibit an explicit coun terexample showing that it is not. (c) Determine if the binary operation has any left identity elements, and list them. (d) Determine if the binary operation has any right identity elements, and list them. In (c) and (d) you can just give a list, or say “there aren’t any.” No proof is required. You may freely use the arithmetic of R , Q , Z , N without commenting on assumptions like associativity, commutativity, etc. The point of this assignment is not to peer into the structure of arithmetic you know, but...
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This note was uploaded on 02/10/2010 for the course MATH 74 taught by Professor Courtney during the Fall '07 term at Berkeley.
 Fall '07
 COURTNEY
 Math

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