Consider transaction T$1$ that sets x$=0$ and y $=1$ and transaction T$2$ that sets x$=2$ and y$=3.$ T$1$ runs first and after recording its intentions in the REDO write$-$ahead log commits.Then T$2$ runs and writes its intentions to the log but a crash occurs before T$2$ writes its commit record to the log$.$ Consider two cases. In one case, the part of the log containing intentions of T$1$ was garbage collected before the crash. In the second case, the log garbage collection did not run yet after T$1$ committed. Explain what will be the state of x and y on disk after recovery in each case?