CMSC 203, Section 0401

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• CMSC 203, Section 0401
• Discrete Structures
• Fall 2004
• Matt Gaston
• mgasto1_at_cs.umbc.edu
• http//www.csee.umbc.edu/mgasto1/203

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Course Overview

• Course Syllabus
• Academic Integrity
• Course Schedule
• Survey

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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 Morgans 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