Exercise 2.3.3 Let M be the Kripke structure , where W, I, and J are defined as follows:

W = {t, u, v, x, y, z}

I: PropVar -> given by:

I(p) = {x, y, z}

I(q) = {x, y, t}

I(r) = {y, t, u, z}

J: PName -> given by:

J(A) = { (w,w) | w E W} U { (x,y), (x,z), (z,t), (y,v), (v,y), (v,x)}

J(B) = { (x,w) | w E W} U { (y,t), (z,t), (t,v)}.

Calculate each of the following sets.

a. EM [[ p q) r]]

b. EM [[A says (p r)]]

c. EM [[A says (B says q)]]

d. EM [[B says (B says q)]]

e. EM [[A controls (B says q)]]

f. EM [[A controls (B controls q)]]