Which one of the following statements are not correct?
$S1$: $3$NF decomposition is always lossless join and dependency preserving.
$S2$: $3$NF decomposition is always lossless join but may or may not be dependency preserving.
$S3$: BCNF decomposition is always lossless join and dependency preserving.
$S4$: BCNF decomposition is always lossless join but may or may not be dependency preserving.
- Only $S1$
- Only $S4$
- Both $S1$ and $S4$
- Both $S2$ and $S3$