We are given the following Markov network structure, $H.$

a$.$ Find a minimal I$-$Map Bayesian network structure $G_1$ for $H.$ Use the variable order of $A,B,C,D,E.$

b$.$ Find a minimal I$-$Map Bayesian network structure $G_2$ for $H.$ Use the variable order of $E,D,C,B,A.$

c$.$ Is $G_1$ a P$-$Map for $H?$ If not, which independencies are missing?

d$.$ Is $G_2$ a P$-$Map for $H?$ If not, which independencies are missing?