Denote by the set of all variables in the system (i.e. variables that correspond to some node in the Network)

- a)
- [2 P]
Show that , i.e. a variable is conditionally independent of all other variables given its Markov Blanket. Use the fact that is conditionally independent of all its non-descendants given its parents (this is true by construction of the Bayesian Network). Be sure to specify what a "non-descendant" node is.

- b)
- [2 P]
Show (e.g. by counter example) that cannot be left out of the definition of a Markov Blanket. So you need to show that there is a network in which some is not conditionally independent of all other nodes given .