Construct an Aumann model of incomplete information for each of the following situations, and specify a state of the world in that model which corresponds to the situation (there are several possible ways of including higher-order beliefs in each model):

(a) Mary gave birth to a baby, and Herod knows it.

(b) Mary gave birth to a baby, and Herod does not know it.

(c) Mary gave birth to a baby, Herod knows it, and Mary knows that Herod knows it.

(d) Mary gave birth to a baby, Herod knows it, but Mary does not know that Herod knows it.

(e) Mary gave birth to a baby, Herod does not know it, and Mary does not know whether Herod knows it or not.