Recall the Consistency of Transactions: Actions and locks must relate in the expected ways:

A transaction can only read or write an element if it previously was granted a lock on the element and

hasn't yet released the lock.

If a transaction locks an element, it must later unlock that element.

For each of the transactions described below, suppose that we insert one lock and one unlock action for each

database element that is accessed. Calculate how many sequence orders of the lock, unlock, read, and write

actions are in the following cases. Please show your working. $($Note: the order of the data access operations

shall not be affected.$)$

$T_1$:$r_1(A),w_1(B)$

$T_2$:$r_2(A),w_2(A),w_2(B).$

$($A$)$ Consistent and two$-$phase locked.

$($B$)$ Consistent, but not two$-$phase locked.

$($C$)$ Inconsistent, but two$-$phase locked.

$($D$)$ Neither consistent nor two$-$phase locked.