CS173: Discrete Mathematical Structures
Spring 2006
Homework #1
Due Sun 22/01/06, 8AM.
0)
a) Post your name to the class newsgroup under the “Problem #1” thread.
b) Post your favorite saying/maxim (not offensive!!!) in the wiki site at https://www-
s.cs.uiuc.edu/wiki/cs173/index.php/Main_Page (go to the 'Welcome! Post your favorite saying
(adage/maxim) here!' section and click on the Saying link).
1) Are the following pairs of propositions equivalent?
a) Today is not Tuesday – Today is Moday.
b) The book does not cost 3 dollars – The book costs either less than 3 dollars or more than 3
dollars.
c) It is neither windy nor cold in Urbana – It is both not windy and not cold in Urbana.
2) Which of the following are tautologies? Which are contradictions?
a) (p→q)∧(
¬
q→p)
b) (p→q)∧(
¬
p→
¬
q)
c) (p→q)∨(q→p)
d) (p→q)→(q→p)
e) (p→q)→(
¬
q→
¬
p)
3) You are given the following prepositions:
•f - passed the final
•m1 - passed midterm1
•m2 - passed midterm2
•h - submitted all your homework.
•A - get an A
•r - retake the course.
Find two logically nonequivalent specifications of the statement below (this demonstrates the possible
ambiguity of programming languages)
If you pass the final and one of the two midterms then if you have submitted all your
homework, then you then you get an A, else you will have to retake it.
4) Express the following system specifications using propositions. Are these system specifications
consistent?
“If the file system is not locked, then new messages will be queued. If the file system is not
locked, then the system is functioning normally, and conversely, If new messages are not
queued, they will be sent to the message buffer. If the file system is not locked, then new
messages will be sent to the message buffer. New messages will not be sent to the message
buffer.”
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