CECS 228 -- Discrete Structures with Computer Science Applications I
REVIEW TOPICS FOR MIDTERM 1
The midterm 1 is scheduled for Thursday, October 14, 2004 at 5:30pm. The midterm is a closed-book
and closed-notes exam and will cover the following material:
Chapter 1: 1.1 -- 1.8
Symbols and notations on logic, sets, and functions.
Chapter 1: 1.1 -- 1.8
๏ฑLogic, propositions, propositional equivalences, predicates and quantifiers
๏Construct and break down compound propositions and predicates with or without
quantifiers
๏Convert between English sentences and propositions/predicates
๏Identify if a given set of specifications is consistent
๏Solve puzzles from a set of given statements
๏ฑRules of inference for propositions and quantifiers
๏Rules of inference for propositional logic and for quantified statements
๏Apply rules of inference in an argument
๏Construct an argument using rules of inference to show the conclusion is valid
๏Find all possible conclusions one can deduce from a set of statements using rules of
inference
๏Find fallacies in an invalid argument
๏ฑSets and set operations
๏Define a set in various notations and perform set operations
๏Find the Cartesian product of sets, and the power set of a given set
๏Represent a set in computer programs, and the corresponding operations
๏Recognize well-known set identities, and find out the relationship between two sets
(equal, subset, etc.)
๏Prove set identities using membership tables, set definitions, and known set identities
๏ฑFunctions
๏Recognize if a given mapping is a function
๏Find the domain and range of a function, and whether a function is 1-1, onto, or both
๏Given the domain and codomain and find all possible functions that are 1-1, onto, both,
and no restrictions
๏Find composite and inverse functions
๏Use and graph special functions including the floor and ceiling functions
Shui Lam (Fall 2004)
