Determine whether or not the definition of * On $Z^{+}$ , define * by $a \cdot b = ∣ a - b ∣$ gives a binary operation. In the event that * is not a binary operation give justification of this. Here, $Z^{+}$ denotes the set of all non-negative integers.

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Determine whether or not the definition of * On

Z^{+}

, define * by

a \cdot b = ∣ a - b ∣

gives a binary operation. In the event that * is not a binary operation give justification of this. Here,

Z^{+}

denotes the set of all non-negative integers.

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Determine whether or not the definition of * On

Z^{+}

, define * by

a \cdot b = ∣ a - b ∣

gives a binary operation. In the event that * is not a binary operation give justification of this. Here,

Z^{+}

denotes the set of all non-negative integers.

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