Math Challenges

Problem #8

Binary Operations

Recall that a binary operation on a set S takes two elements of set S and maps them to an element of set S. Are the following considered binary operations?

\[ \displaylines{1)S=\mathbb{Z},a\ast b=a^4b^3\\ 2)S=\mathbb{Z},a\ast b=\frac{a^2}{b}} \]

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