Which of the following statements is true?
$D_1$: The decomposition of the schema R(A, B, C) into R$_1$(A,B) and R$_2$(A,C) is always lossless
$D_2$: The decomposition of the schema R(A, B, C, D, E) having AD $\rightarrow$ B, C $\rightarrow$ DE, B $\rightarrow$ AE, and AE $\rightarrow$ C, into R$_1$(A,B, D) and R$_2$(A, C, C, D, E) is lossless
- Both $D_1$ and $D_2$
- Neither $D_1$ nor $D_2$
- Only $D_1$
- Only $D_2$