11. 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 probability on a set of variables (e.g., asking for the P(X, Y ∣ e))?