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 $a * b = ab$.
Here $, Z^+$ denotes the set of all non $-$ negative integers.

✓

Answer

$\text{a, b}\in\text{Z}^{+}$
$\Rightarrow\ \text{ab}\in\text{Z}^+$
$\Rightarrow\ \text{a}\ ^*\ \text{b}\in\text{Z}^+$
Therefore,
$\text{a}\ ^*\ \text{b}\in\text{Z}^+,\ \forall\ \text{a, b}\in\text{Z}^+$
Thus, $*$ is a binary operation on $Z^+$.

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