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Topics for Final Exam:
This sheet is intended to help you prepare for the final exam in this course. The exam will
cover the entire course, however it will emphasize topics learned in the second half of the course,
in chapters 5, 8, 9, 10, 11, 12 and 16.
You should study your class notes, textbook readings, handouts, and homeworks. You will be provided with
list of theorems from the back of your textbook and you may bring notes on one side of one
8.5" x 11" piece of paper.
The following topics have been covered since the first midterm. You should also review topics from the first half of the course (see midterm review). Each of the following topics may appear on the exam.
Chapter 5: Word problems and Circuits Word Problems Given a set of assertions and a conclusion, either: Prove the conclusion, or Find a counter-example Digital Circuits Logic Gates (AND, OR, INVERTER, NAND, NOR) Constructing a logical expression from a circuit. Construct a truth table from a circuit. Construct a circuit that implements a logical expression. Universal Building blocks. Chapter 8: Quantification Basic types in programming languages Quantification Linear notation for quantification Quantification with more than 1 variable Bound vs. free variables. Textual substitution in quantifications Axioms and Theorems for quantification Range Splitting Chapter 9: Predicate calculus Universal Quantification Axioms and theorems for universal quantification Existential quantification Axiom, Generalized DeMorgan Axioms and Theorems for existential quantification Translation from English into predicate logic Word problems and predicate logic Chapter 10: Predicates and programming Program specification Weakest precondition Definition For assignment statements Proving an assignment is correct. Assignment derivation, given pre and post conditions. Conditional statements Proving then and else statements General IF statement Chapter 11: Sets Denoting Sets Set Comprehension Translating set comprehensions into English descriptions Translating English descriptions into set comprehensions Set Operations Union, Intersection, difference Properties of operations Power sets Bags Chapter 12: Mathematical Induction Proof by induction Base Case Inductive Case Inductive Hypothesis Inductive definitions Loops Checklist for proving loop correctness Loop Invariant Proving Loop Termination Bound function for loop termination Chapter 16: Counting The Rule of Sum The Rule of Product The Pigeonhole Principle Permutations Finding P(n, r) Combinations Finding C(n, r)