1. Fill in the blanks with True or False. Justify your answers by showing how you evaluate each sentence.

A. If A is False and B is True, then "A |= B" is .................... B. (a: (a=a) negative(a) ) (a: a=a) is ......................

2. If X and Y are two propositional symbols, then {x=.........., Y=.........} would be a model in which the knowledge base (i.e., X Y X Y) is true. Justify your answer by showing how the model possibly produces a True value for the knowledge base (aka KB).

3. A knowledge base consists of W, X, Y, and Z as propositions. How many models (i.e., those which result in a true value) are there for the following sentence in the knowledge base?

W X Y Z

4. There are some difficult tests in a course in such a way that no participant got an "A" on every test. What is the logical representation of the above sentence in first order logic?

You can assume that: p = a participant

t = a test

Participant(p) = participate in the course Test(t) = taking a test

Get_A(p,t) = participant gets an "A" in a test

5. There is a record in an agent's knowledge base stating that: " if A happens then B happens and if A does not happen then C will happen, and C does not happen". What entailment can be made considering the record in the knowledge base.

6. What is the CNF of X (Y Z)?