1. [15 marks] Consider the following set of known facts and rules for a production system. (Check the Forward and Backward Chaining slides in the Rule-Based Systems file in Module 3 for an example).

Facts (known to be true): L, M, N

Rules:

1. L O (means that if L is true then O is true)

2. M & N Q (means that if M and N are both true then Q is true)

3. N R

4. P & Q S

5. R U

6. P W

7. T & W Z

8. S & U V

9. O T

10. M & O P

11. R & X Y

b. [5 marks] Using backward chaining, prove that Z is true. Which rules and in what order, would fire to accomplish this? What facts do we know after backward chaining has completed?