UMBC CMSC 203, Section Fall CMSC 203, Section 0401 Discrete Structures Fall 2004 Matt Gaston

UMBC CMSC 203, Section Fall Course Overview Course Syllabus Academic Integrity Course Schedule Survey

UMBC CMSC 203, Section Fall Lecture 1 Logic and Propositional Equivalences Ch

UMBC CMSC 203, Section Fall Ex – 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 Fall Ex 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 Fall Ex 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 Fall 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)

UMBC CMSC 203, Section Fall Ex – 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.