State whether each of the following statements is true or false. Provide a proof if the statement is true or a counterexample if the statement is false.

(a) If \(\widetilde{X}\) is a fair game with respect to \(\widetilde{Y}\), and \(\widetilde{Y}\) is a fair game with respect to \(\widetilde{X}\), then \(\widetilde{X}\) and \(\widetilde{Y}\) are independent.

(b) If \(\underset{\sim}{\tilde{Y}}\) and \(\underset{\sim}{\widetilde{Y}}\) have zero means and zero covariance, then \(\tilde{X}\) is a fair game with respect to \(\widetilde{Y}\) and \(\widetilde{Y}\) is a fair game with respect to \(\widetilde{X}\).

(c) For jointly normally distributed random variables, zero covariance implies independence.