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.

Answer

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free