There are 5 statements: 

A. Statement B, C, or D is false.

B. If statement C is false, then statement D is true.

C. It is not true that statement E is false.

D. Statements B and C have the same truth values.

E. If statement A is true, then C is false. 

There's only 1 false statement, the rest it true. Which statement is false?

The answer turned our to be A. I understand why statements C, D, and E are true, but if statement B is true then wouldn't statement D be false?