Q

# 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. On Z + , define ∗ by a ∗ b = | a – b |

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.

(iv) On $Z^+$, define ∗ by $a * b = | a - b |$

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(iv) On $Z^+$, define ∗ by $a * b = | a - b |$

We can observe that for $a,b \in Z^+$,there is a unique element $| a - b |$  in $Z^+$.

This means * carries each pair $(a,b)$  to a unique element $a * b = | a - b |$ in $Z^+$.

Therefore,* is a binary operation.

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