This preview shows page 1. Sign up to view the full content.
CS 2603 — A
PPLIED
L
OGIC
FOR
H
ARDWARE
AND
S
OFTWARE
11/19/07
Midterm Examination 2
Fall 2007
1
Assume that
f
and
g
are predicates that both have the same universe, nonempty universe of
discourse. Use the inference rules of natural deduction (not the equations of Boolean algebra)
to prove the following theorem.
(∃
x
.(
∀
y
.(
f
(
x
)
∧
g
(
y
))))
–
((
∃
x
.
f
(x))
∧
(
∀
x
.
g
(
x
)))
2
Assume that
f
and
g
are predicates that both have the same universe of discourse. Use the
Boolean equations of predicate calculus to prove that the following equation is true.
((
∀
x
.(
f
(
x
)
∨
g
(
x
)))
∧
(
∀
x
.
g
(
x
)))
=
(
∀
x
.
g
(
x
))
3
Prove the following proposition.
∀
n
.P(
n
), where P(
n
)
≡
(
length
(
zipWith z
[
x
1
, x
2
, .
.. x
n
] [
y
1
, y
2
, .
.. y
n
]) =
n
)
4
Suppose that the following equations are true
f[x] = [ ]
{f 1}
f(x
1
: (x
2
: xs)) = x
1
: (f(x
2
: xs))
{f 2}
Prove the following proposition.
∀
n
This is the end of the preview. Sign up
to
access the rest of the document.
This test prep was uploaded on 04/08/2008 for the course CS 2603 taught by Professor Rexpage during the Spring '08 term at The University of Oklahoma.
 Spring '08
 RexPage

Click to edit the document details