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We know that the set of integers Z forms a ring under + (addition) and x (multiplication) operations. Let's replace x with another binary

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We know that the set of integers Z forms a ring under + ("addition") and x ("multiplication") operations. Let's replace x with another binary operation: max (taking a maximum of the two operands and acting as our new "multiplication"). Does Z still form a ring under + and max operations? Justify your answer.

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