# Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this: (v)On $Z^+,define \;\ast\;by\;a\;\ast\;b=a.$

Note: This is part 5 of a 5 part question, split as 5 separate questions here.

Toolbox:
• A binary operation $∗$ on a set $A$ is a function $∗$ from $A \times A$ to $A$. Therefore, if $a,b \in A \Rightarrow a*b \in A\; \forall\; a,b, \in A$
Given On $Z^+$ defined $*$ by $a*b=a$
For each pair of element $a,b \in Z_+,*$ carries (a,b) to unique element $a \in Z+$
Therefore it is a binary operation.
edited Mar 19, 2013