# Q.1 Determine whether or not each of the definition of ∗ given below gives a binary operation. In the event that ∗ is not a binary operation, give justification for this(v) On  $Z^+$ , define ∗ by $a * b = a$

(v) On  $Z^+$ , define ∗ by $a * b = a$
* carries each pair $(a,b)$  to a unique element $a * b = a$ in  $Z^+$.