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)