Exercise 6.7 Explain how to extend VE to allow for more general observations and queries. In particular, answer the following:

(a) How can the VE algorithm be extended to allow observations that are disjunctions of values for a variable (e.g., of the form X = a ∨ X = b)?

(b) How can the VE algorithm be extended to allow observations that are disjunctions of values for different variables (e.g., of the form X = a ∨ Y = b)?

(c) How can the VE algorithm be extended to allow for the marginal probability on a set of variables (e.g., asking for the marginal P(XY|e))?