QUESTION 1 Assuming predicates parent(P, Q) and female(P) and constants joan and kevin, with the obvious meanings, express each of the following sentences in first-order logic. (You may use the abbreviation 1 to mean there exists exactly one.) a. joan has a daughter (possibly more than one, and possibly sons as well).

b. joan has exactly one daughter (but may have sons as well).

c. joan has exactly one child, a daughter.

d. joan and kevin have exactly one child together.

e. joan has at least one child with kevin, and no children with anyone else.

QUESTION 2 Given the following relationships in Prolog clauses: father(X,Y) /* X is the father of Y */

mother(X,Y) /* X is the mother of Y */

male(X) /* X is male */

female(X) /* X is female */

parent(X,Y) /* X is a parent of Y */

diff(X,Y) /* X and Y are different */ Write Prolog clauses to define rules for the following relationships: is_mother(X) /* X is a mother */

is_father(X) /* X is a father */

is_son(X) /* X is a son */

sister_of(X,Y) /* X is a sister of Y */

grandpa_of(X,Y) /* X is a grandfather of Y */

sibling(X,Y) /* X is a sibling of Y */

For example, given the rules for female, sibling, and parent, we could write a rule for aunt. aunt(X,Y) :- female(X), sibling(X,Z), parent(Z,Y). or aunt(X,Y) :- sister_of(X,Z), parent(Z,Y). /* if we had sister_of rule. */ Test your rules by entering some facts of family relationships.

Q-3. Define in your own words the following terms: state, state space, search tree, search node, goal state, and branching factor. ( ARTIFICIAL INTELLIGENCE)

Q-4.

J K L M N O P R Follow the example in the book and discussed in the class. Do a "Hand run" of the backtracking algorithm on the graph in the Figure above. Begin from state A. Keep track of the successive values of NSL, SL, CS and DE. Assume there is no goal state in the search space