Addition of real numbers is associative: (a + b) + c = a + (b + c). So is multiplication: (ab)c = a(bc). But not every operation is associative.
a) Subtraction is not associative; in general (a - b) - c = a - (b - c). When is it associative?
That is find all solutions to (a - b) - c = a - (b - c).
b) Find all solutions to (a/b)/c = a/(b/c).
c) What about exponentiation? Find all solutions in positive real numbers to (a∧b)∧c =a∧(b∧c). If stuck, Consider more restricted questions, such as what are all the solutions to this equation if a, b, c are positive integers .