5 The binary operation * is defined as
$$a * b = a + b + 4 ( \bmod 6 )$$
where \(a , b \in \mathbb { Z }\).
5
- Show that the set \(\{ 0,1,2,3,4,5 \}\) forms a group \(G\) under *.
5 - Find the proper subgroups of the group \(G\) in part (a).
5 - Determine whether or not the group \(G\) in part (a) is isomorphic to the group \(K = \left( \langle 3 \rangle , \times _ { 14 } \right)\)
[0pt]
[3 marks]