## Problem Set 2

Assigned: Feb. 12
Due: Mar. 5. NOTE EXTENDED DUE DATE

### Problem 1

What is the result of doing alpha-beta pruning in the game tree shown below?

### Problem 2

Use propositional resolution to prove (a) from (b-e).
• a. (not p) < = > (q ^ r)
• b. p V q.
• c. p V w.
• d. w => r.
• e. p => (not (q ^ r))

### Problem 3

Let L be a first-order languge where the entities are people and places. L contains the following non-logical symbols:
a(X) -- X is an adult.
b(X) -- X is a baby.
c(X,Y) -- X is taking care of Y.
p(X,L) -- X is at place L.
j,k -- Constants. Joe and Karen.
g -- Constant. The playground.
Express the following sentences in L:
• 1. If B is a baby, then there exists an A who is taking care of B.
• 2. If A is taking care of B, then for any place L, A is at L if and only if B is at L.
• 3. If A is taking care of B, then A is an adult and B is a baby.
• 4. If A is in the playground and A is an adult, then there exists a baby B such that A is taking care of B. (That is, adults are only allowed in the playground if they are taking care of a baby.)
• 5. Everyone who is taking care of Joe is also taking care of Karen.
• 6. Joe and Karen are babies.
• 7. If there are no babies in the playground, then there are no adults in the playground.
• 8. For every place L, if Joe is at L then Karen is at L.