Consider the following operators:

1. :) where aa :)b=4a+7b+2b=4a+7b+2
2. where ab=6ab=6
3. where ab=2a+2bab=2a+2b
4. where ab=a+5bab=a+5b
5. where ab=3abab=3ab
6. where ab=a2+b+8ab=a2+b+8
7. where ab=a2+b2ab=a2+b2
8. @ where aa@b=7bb=7b
9. # where aa#b=b=the smaller value of aa or bb
10. Prove any one of the operations is commutative.
11. Give a counterexample for one of the operations that is not commutative.