Question $3.(40$ marks$)$

Consider the three transactions, $T1,T2,$ and $T3,$ and

the schedules S$1$ and S$2$ given below.

$T1$:$r1(x)$;$r1(y)$; $w1(x)$; $c1$

$T2$:$r2(x)$;$r2(z)$; $w2(z)$; $c2$

$T3$:$r3(z)$;$r3(x)$; $w3(x)$; $c3$

$S1$:$r1(x)$;$r1(y)$; $r2(x)$; $r2(z)$;$r3(z)$;$r3(x)$; $w2(z)$; $c2$; $w1(x)$;

$c1$; $w3(x)$; $c3.$

$S2$:$r1(x)$;$r1(y)$;$r2(x)$; $r2(z)$; $w1(x)$;$r3(z)$;$r3(x)$; $w3(x)$; $c3$;

$w2(z)$; $c2$; $c1.$

Notes: $r1(x)$ represents transaction $1$ read $x$; $w2(y)$

represents transaction $2$ write $y$;$c3$ represents

transaction $3$ commits.

$(1)$ Draw the serializibility graphs for S$1$ and S$2$

and state whether each schedule is serializable

or not.$[20$ marks$]$

$(2)$ Determine whether the schedule is

recoverable$/$nonrecoverable$,$ cascadeless, or

strict.$[20$ marks$]$