Problem $1$:

$2\mathrm{.}1.$ Draw the reachability graph for the Petri Net.

$2\mathrm{.}2.$ Write down the incidence matrix $\backslash ($ N $\backslash )$ for the Petri Net.

$2\mathrm{.}3.$ Which properties can be checked with the help of the incidence matrix $\backslash ($ N $\backslash )?$ Give the conditions under which those properties hold.

$2\mathrm{.}4.$ Check the

a$.$ liveness,

b$.$ reversibility,

c$.$ deadlock$-$freeness,

of the Petri Net. Give reasoning for your answer.

$2\mathrm{.}5.$ Is the Petri Net "safe"? What does that term mean?