I$\text{'}$m not sure how the Precedence Graph $($a$)$ is supposed to be setup, nor how to determine if it's always determinate $($b$).$ I upvote for clear answers!!

Consider a system of six processes P$=\{$P$\_(1),$cdots,P$\_(6)\}.$

Associated with the system are $6$ memory cells M$=\{$M$\_(1),$cdots,M$\_(6)\}.$

The domain and range for each process is given in the following table:

In addition, you are given the following precedence relation:

$->=\{($P$\_(1),$P$\_(3)),($P$\_(1),$P$\_(4)),($P$\_(2),$P$\_(4)),($P$\_(3),$P$\_(5)),($P$\_(4),$P$\_(5))\}$

a$->$ necessary elements to

make it determinate.