Q$4.$ Consider the following two transactions:

Tis: read$(A).$

read$(B).$

$ifA=0$ then $B$;$=B+1$ :

write $(B).$

I $Ti4$: read$(B)$;

read$(A)$:

$ifB=0$ then $A$:$-A+1$ :

write$(A).$

Let the consistency requirement be $A=0vvB=0,$ with $A=B=0$ as the initial values.

a$)$ Show that every serial exceution involving these two transactions preserves the eonsistency of the database.

b$)$ Show a concurrent execution of $T_1$ and $T_1$ that produces a nonserializable schedule.

c$)$ Is there a concurrent execution of $T_1$ and $T_4$ that produces a serializable schedule?

d$)$ Add lock and unlock instructions to transactions $gra{d}_1$ and $T_{14}$ so that they observe the two$-$phase locking protocol. Can the execution of these transactions result in a deadlock?