In the figure, [] and () indicate that it is the MAX and MIN player's turn, respectively, and the numbers at the bottom show the payoff for the given terminal positions. Which State MAX will move to using the mini-max and alpha-beta algorithms?

[ ]

/ \

(A) (B)

/ \ / \

[C] [D] [E] [F]

0 2 -2 4

b) Hill climbing with random restarts is guaranteed to find the global optimum if it runs long enough on a finite state space.T or F

c) Which of the following are used in typical chess programs such as Deep Blue?

	a.	alpha-beta pruning
	b.	forward chaining
	c.	genetic algorithms
	d.	trueth tables

d) A and B are propositions. Given the equality P(A|B) = x and the following statements. (~A means negation A)

(i) P(B ->A) = x

(ii) B ->P(A) = x

(iii) P(A| ~B) = 1 -x

(iv) P(~A|B) = 1-x

Which of the above statements are necessarily true?

	a.	only (i) and (ii)
	b.	only (i) and (iii)
	c.	only (iv)
	d.	only (ii) and (iv)