Determine whether each of the following statements is true or false. If the statement is false, provide a counterexample.
(a) [a] = [a] for all a ∈ Z.
(b) [a] = [a] for all ∈ R.
(c) [a] = [a] - 1 for all a ∈ R - Z.
(d) - [a] = [-a] for all a ∈ R.