Transcript CMSC 203, Section 0401 Discrete Structures Fall 2004 Matt Gaston [email protected] http://www.csee.umbc.edu/~mgasto1/203 UMBC CMSC 203, Section 0401 -- Fall 2004

CMSC 203, Section 0401
Discrete Structures
Fall 2004
Matt Gaston
[email protected]
http://www.csee.umbc.edu/~mgasto1/203
UMBC CMSC 203, Section 0401 -- Fall 2004
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Course Overview
• Course Syllabus
• Academic Integrity
• Course Schedule
• Survey
UMBC CMSC 203, Section 0401 -- Fall 2004
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Lecture 1
Logic and
Propositional Equivalences
Ch. 1.1-1.2
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Ex. 1.1.7 – Converse, Contrapositive, Inverse
• The home team wins whenever it is raining.
• Rewrite: If it is raining, then the home team wins.
• Converse: If the home team wins, then it is raining.
• Contrapositive: If the home team does not win, then it is
not raining
• Inverse: If it is not raining, then the home team does not
win.
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Ex. 1.1.10 - Translation
• “You cannot ride the roller coaster if you are under
four feet tall unless you are older than 16 years
old.”
• Propositions:



q is “You cannot ride the roller coaster”
r is “You are under four feet tall”
s is “You are older than 16 years old”
• (r  s)  q
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Ex. 1.1.12 - Consistency
•
System specification:



“The diagnostic message is stored in the buffer or it is retransmitted.”
“The diagnostic message is not stored in the buffer.”
“If the diagnostic message is stored in the buffer, then it is retransmitted.”
•
•
p is “The diagnostic message is stored in the buffer”
q is “The diagnostic message is retransmitted”
•
Specification:



pq
p
pq
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Logical Equivalences
• Tables 5, 6, 7 in the Text (pg. 24)

Identity, domination, idempotent, double negation, commutative,
association, distributive, absorption, negation
• De Morgan’s Laws


(p  q)  p  q
(p  q)  p  q
• Implications

p  q  p  q
• Biconditional

p  q  (p  q)  (q  p)
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Ex. 1.2.6 – Constructing Equivalences
Show that (p  q)  (p  q) is a tautology.
(p  q)  (p  q)  (p  q)  (p  q)
(by implication)
 (p  q)  (p  q) (by De Morgan)
 (p  p)  (q  q) (by assoc. and commutative)
TT
T
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