1. UMBC CMSC 203, Section 0401 -- Fall 20041 CMSC 203, Section 0401 Discrete Structures Fall 2004 Matt Gaston mgasto1@cs.umbc.edu http://www.csee.umbc.edu/~mgasto1/203

2. UMBC CMSC 203, Section 0401 -- Fall 20042 Course Overview Course Syllabus Academic Integrity Course Schedule Survey

3. UMBC CMSC 203, Section 0401 -- Fall 20043 Lecture 1 Logic and Propositional Equivalences Ch. 1.1-1.2

4. UMBC CMSC 203, Section 0401 -- Fall 20044 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.

5. UMBC CMSC 203, Section 0401 -- Fall 20045 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

6. UMBC CMSC 203, Section 0401 -- Fall 20046 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

7. UMBC CMSC 203, Section 0401 -- Fall 20047 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)

8. UMBC CMSC 203, Section 0401 -- Fall 20048 Ex. 1.2.6 – Constructing Equivalences (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 Show that (p  q)  (p  q) is a tautology.