Determine whether or not the definition of * given below gives a … - Vidyadip

Question

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

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Answer

On $Z^+, *$ is defined by $a * b = a - b$
It is not a binary operation as the image of $(1, 2)$ under $*$ is $1 * 2 = 1 - 2$
$=-1\notin\text{Z}^{+}$

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