a$.$ In a certain concurrent schedule S $1,$ we have three transactions $T1,T2,$ and T $3.$ These transactions operate on data items $A,B$ and C $.$ The interleaving of operations of these transactions in S $1$ is given below.

Schedule S$1$:

$\{r_2(B)$;$r_3(A)$;$w_3(A)$;$r_3(B)$;$r_1(C)$;$r_2(C)$;$w_1(C)$;$w_3(A)$;$r_2(A)$;$w_2(B)$;$r_1(A)$;$w_1(A)$;$\}$

Note: Here, $r_2(A)$; $-$ means that the transaction$-2$ reads data item A

$w_2(A)$; means that the transaction$-2$ updates data item $A$

Check if the above schedule is conflict serializable, by drawing a precedence graph.

Note: For the correct graph you get $2$ Marks and for the correct final answer mentioning conflict serializable or not $1$ mark. $3$ Marks $1$

$($b$)$ In a certain concurrent schedule $S2,$ we have three transactions $T1,T2,$ and T $3.$ These transactions operate on data items $A,B,$ and C $.$ The interleaving of operations of these transactions in $S2$ is given below.

Schedule S$2$ :

$\{r_1(A)$;$r_1(B)$;$w_1(B)$;$r_2(B)$;$w_2(B)$;$r_2(A)$;$r_3(B)$;$w_3(B)$;$C_3$;$r_2(C)$;$C_2$;$r_1(C)$;$w_1(C)$;$C_1$;$\}$

Note: Here, $,r_2(A)$; $-$ means that the transaction$-2$ reads data item $A$

$w_2(A)$; $-$ means that the transaction$-2$ updates data item A

$C_2$;$-$ means transaction T $2$ commits.

Now, check S $2$ is recoverable or not. Give your reason.

Marks