6. Consider the set of elements a, b, c, d and operations and with tables below. (i) Examine this system with respect to the structural properties and the possi- bility that the system defines "an algebra." For example, it is obvious that the algebra is closed under the operations and so we have closure for both op- erations. What about the other structural properties, such as the commutative and associative properties and the existence of identities and inverses does this algebra have? (ii) If possible, solve the equations ax + b = c, andx² + (x - b)(xd) = x² justifying each step as in the first problem above. a b C d a b C d a a b C d a a a a a b b C d a b a b C d C C d a b C a C a C d d a b C d a d C b