- A binary operation ★ on the set of non-negative integers, \(\mathbb { Z } _ { 0 } ^ { + }\), is defined by
$$m \star n = | m - n | \quad m , n \in \mathbb { Z } _ { 0 } ^ { + }$$
- Explain why \(\mathbb { Z } _ { 0 } ^ { + }\)is closed under the operation
- Show that 0 is an identity for \(\left( \mathbb { Z } _ { 0 } ^ { + } , \star \right)\)
- Show that all elements of \(\mathbb { Z } _ { 0 } ^ { + }\)have an inverse under ★
- Determine if \(\mathbb { Z } _ { 0 } ^ { + }\)forms a group under ★, giving clear justification for your answer.