CMSC 203 Section 0401 Discrete Structures Fall 2004
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CMSC 203, Section 0401 Discrete Structures Fall 2004 Matt Gaston mgasto 1@cs. umbc. edu http: //www. csee. umbc. edu/~mgasto 1/203 UMBC CMSC 203, Section 0401 -- Fall 2004 1
Course Overview • Course Syllabus • Academic Integrity • Course Schedule • Survey UMBC CMSC 203, Section 0401 -- Fall 2004 2
Lecture 1 Logic and Propositional Equivalences Ch. 1. 1 -1. 2 UMBC CMSC 203, Section 0401 -- Fall 2004 3
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. UMBC CMSC 203, Section 0401 -- Fall 2004 4
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 UMBC CMSC 203, Section 0401 -- Fall 2004 5
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 UMBC CMSC 203, Section 0401 -- Fall 2004 6
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 • Implications § p q • Biconditional § p q (p q) (q p) UMBC CMSC 203, Section 0401 -- Fall 2004 7
Ex. 1. 2. 6 – Constructing Equivalences Show that (p q) is a tautology. (p q) (by implication) ( p q) (p q) (by De Morgan) ( p p) ( q q) (by assoc. and commutative) T T T UMBC CMSC 203, Section 0401 -- Fall 2004 8
