All of the Following Statements Are True About the Real $\frac{P^{*}}{P}$

All of the following statements are true about the real exchange rate,given by the relation R_r = R_n ( $\frac{P^{*}}{P}$ ) ,except

A) a greater change in P (domestic price) compared to a change in $P^{*}$ 1 (foreign price) necessitates a rise in the nominal rate, R_n ,to keep the real rate unchanged.
B) a pegged exchange rate system requires tight control of the money supply.
C) there is a one-to-one correspondence between the real and nominal exchange rates.
D) an expansionary monetary policy raises the real exchange rate.
E) the real exchange rate would be the same as the nominal exchange rate only if the difference between domestic and foreign inflation rates is zero.