Let F be the set of all real-valued functions having as domain the set  R. of all real numbers. Example 2.7 defined the binary operations +, -, •, and o on F. Either prove the given statement or give a counterexample.

If * and *' are any two binary operations on a set S, then a* (b *' c) =(a * b) *' (a* c) for all a,b,c ∈ S.