Prove that if * is an associative and commutative binary operation on a set S, then (a * b) *(c * d)=[(d * c) * a] * b for all a, b, c, d ∈S. Assume the associative law only for triples as in the definition, that is, assume only for all x, y, z ∈S. (x * y) * z=x *(y * z) | Numerade

Every commutative binary operation on a set having just two elements is associative. 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. In Exercises 29 through 35, either prove the given statement or give a counterexample. | Numerade

Binary Division & Multiplication: Rules & Examples