<PRE><B>Question 1166868</B>
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Response revised/corrected....&lt;br&gt;
The two inputs are integers; and the output is always an integer.&lt;br&gt;
That makes * a binary operation on the set of integers.&lt;br&gt;
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Revision...&lt;br&gt;
I wrongly took the given set to be the set of positive integers; in standard nomenclature it is the set of natural numbers.&lt;br&gt;
Even if the set were the set of positive integers, there would be a single counterexample making * NOT a binary operation on the set:
1*1 = 1-1 = 0
But 0 is not a positive integer.&lt;br&gt;
With the set actually being the natural numbers, there are an infinite number of counterexamples.  If either a or b is 0, then a*b = 0-1 = -1; and -1 is not a natural number.&lt;br&gt;
ANSWER: a*b does NOT define a binary operation on the given set.&lt;br&gt;

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