Propositional Logic
1.
(7.5 points)
Write each of the sentences in propositional logic using two propositions p
andq:
a) For you to win the contest (p) it is necessary and su
ffi
cient that you have the only
winning ticket (q)
p
!
q
b) You can access the website (p) only if you pay a subscription fee (q).
p
"
q
c) Getting elected (p) follows from knowing the right people (q).
q
"
p
e) Whenever you get a speeding ticket (q) you are driving over 65 miles per hour (p).
q
"
p
f) You can see the wizard (p) only if the wizard is not in (q) and the wizard is not in only
if you can see the wizard.
p
!
q
2.
(12 points)
Mark would like to determine the relative salaries of his friends based on
two facts. First, he knows that if Francisca is not the highest paid of the three, then John
is. Second he knows if John is not the lowest paid then Martha is paid the most. Is it
possible to determine the relative salaries of Francisca, Martha, and John from what Mark
knows? If so, who is paid the most and who is paid the least. Explain your reasoning.
FHP – Francisca highest paid
FLP – Francisca lowest
paid
JHP – John highest paid
JLP – John lowest
paid
MHP – Martha highest paid
MLP – Martha lowest
paid
~FHP => JHP
~JLP
=> MHP
Assume JHP : that would imply FHP (from 1 using modus tollens);
So ~MHP and therefore JLP which contradicts assumption;
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Assume MHP: therefore ~JHP therefore FHP (from 1 using modus tollens); buththat
contradicts the assumption.
So assume FHP: therefore ~MHP and ~JHP; ~MHP=> JLP; so
So the order is
Francisca, Martha, John
3.
(15 points)
Use resolution refutation to prove:
(
Q
!
¬
P
)
)
!
((
Q
)
!
P
)
!
¬
Q
)
ROBERT – this is a homework question – so it should be discussed only after they hand
it in!!!!
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 GOMES
 Logic, clause, Logical connective, Propositional calculus, QKl

Click to edit the document details