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Q10. Commutativity Consider the abelian group {Z, +}, i.e. the set of all integers with the operation of arithmetic addition. (In fact this is not

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Q10. Commutativity Consider the abelian group {Z, +}, i.e. the set of all integers with the operation of arithmetic addition. (In fact this is not only an abelian group but also a higher-order algebraic structure.) The operation is commutative because the order of the operands does not affect the result. Here is one example: 1+2 = 3 2+1=3 Now consider the tuple {Z, - }, i.e. the set of all integers with arithmetic subtraction. (The term "tuple" used here is deliberately vague - this is some form of algebraic structure.) Select any two distinct (different) elements of this set, but not 0, 1 or 2, and test whether the set operation is commutative following the example above. Show your test calculations. Decide whether this set's operation is commutative or is not and state your decision

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