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Question: exercise 434 besides u and n there is another set...

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Exercise 4.3.4. Besides u and n, there is another set operation called symmetric difference, which is sometimes denoted by the symbol A and is defined as: Given a set A, let G be the set of all subsets of A. Repeat parts (a)-() of Exercise 4.3.3, but this time for the set operation A instead of n. Exercise 4.3.3. Given a set A, let G be the set of all subsets of A. a. Does the set G with the operation n have the closure property? Justify your answer. Does the set G with the operation n have an identity? If so, what is it? Which part of Proposition 4.2.3 enabled you to draw this conclusion? b. C. Is the operation n defined on the set G associative? Which part of d. Is the operation n defined on the set G commutative? Which part of e. Does each element of G have a unique inverse under the operation Proposition 4.2.3 enabled you to draw this conclusion? Proposition 4.2.3 enabled you to draw this conclusion? n? If so, which part of Proposition 4.2.3 enabled you to draw this conclusion? If not, provide a counterexample. Is the set G a group under the n operation? Justify your answer. f.

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