Lecture 2

Learning objectives

After this class, you should be able to:

1. Define terms from set theory, such as: empty set, disjoint sets, powerset, and partition.
2. Given sets, show the results of common set operations, such as: union, intersection, difference, complement, and apply De Morgan's laws.
3. Define functions, relations, and equivalence relations.
4. Given functions, express their asymptotic behavior in big-Oh, big-Theta, and big-Omega notations.
5. Define terms from graph theory, such as: graph, directed graph, walk, path, simple path, cycle, simple cycle, loop, tree, leaf, parent, child, height, and ordered tree.
6. Prove theorems using induction and contradiction.

Reading assignment

1. Section 1.1.
2. Lecture 2 slides on Blackboard.
3. Basic definitions related to languages, on pages 16-17.
4. Read the JFLAP document in the course library on Blackboard, and try some of the grammar exercises.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Section 1.1, exercise #1.
  2. Section 1.1, exercise #10. (Consider some element in the left hand side and show that it is in the rights hand side. Then consider some element in the right hand side and show that it is in the left hand side.)
  3. Section 1.1, exercise #20.
  4. Section 1.1, exercise #23.

• Questions on next lecture's material
  1. What is wR if w = computer?

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Last modified: 29 Dec 2013