COSC3302

      Some Bonus problems (for up to 30 points) due Tuesday,  March 26, 2013

A.                Convert each to CNF and DNF, respectively.                       (8)

            A -> B -> C

            A -> (B -> C)

            (A->B) ^ (B->C) -> (A->C)^(B^C->D)                    

 

B.                 Find clauses of each:                                                               (6)

%x$y (P(x,y) -> Q(x)^R(y))

$x$y%z (P(x,y,z)+Q(z) -> R(x,y))

 

C.                 Explore applications of FSA/RegularExpressions/RegularGrammars

in reasonable details.                                                               (8)

 

D.                Convert the following argument into a wff in Predicate Logic and

            show all the clauses needed for the resolution procedure to establish the validity

of the argument.

And, show that the intended conclusion indeed logically follows

from the set of premises using the Resolution Procedure.

                                                                                                (8)

           

                        P1:       Every millionaire’s adult son is also a millionaire provided that he is both

                                    intelligent and benevolent.

                        P2:       Jim is an adult son of a millionaire.

                        P3:       Jim is benevolent but he is not a millionaire.

                        C:        Therefore, Jim is not intelligent (enough).

 

                        Hints:

1.      Use the following predicate symbols, among others:

a.       mill(x):             x is a millionaire.

b.      int(y):              y is intelligent.

c.       ben(z):             z is benevolent. 

d.      son(x,y):          x is an adult son of y.  

2.      Using above predicate symbols, P1 will turn to the following wff:

     ($ is the Universal Quantifier)

($x$y) mill(x)^int(y)^ben(y)^son(y,x) -> mill(y)