Consider the following operators:

a) :) where a :) b = 8a + 6b + 2

b) where a b = 5

c) where a b = 7a + 7b

d) wherea b = a + 2b

e) wherea b = 4ab

f) wherea b = a2 +b + 6

g) wherea b = a2 + b2

h) @ wherea @ b = 3b

i) # wherea # b = the smaller value ofa orb

1. Prove any one of the operations is associative.
2. Give a counterexample for one of the operations that is not associative.