CSci 271 Lecture Notes
Week Two, Wednesday: Set Operations
Introduction
The union of two sets is the set that contains the elements in one
set or the elements in the other set, or both.
The intersection of two sets is the set containing those elements
in both the sets.
Two sets are disjoint if their intersection is empty.
The difference of two sets is the sets containing those
elements that are in the first set and not in the second set.
The complement of a set (denoted with a bar above the set expression) is
the universal set minus (set difference) A.
Set Identities
See Table 1 on page 50.
Generalized Unions and Intersections
The union of a collection of sets is the set that contains those elements
that are members of at least one set in the collection.
The intersection of a collection of sets is the set that contains those
elements that are members of all the sets in the collection.
Computer Representation of Sets
Using a computer, elements of sets can be represented in terms of the universal
set. We assign a bit position in a sequence to each element of the universal
set. Subsets are then represented by n-length bit strings, where n is the
number of elements in the universal set.
Needless to say, the universal set can be quite large, so using computer words
for this purpose is not practical. A higher level data structure, such as an
array or list can be used.
Homework Assignment
Assigned Wednesday, September 16, due Wednesday, September 23, at beginning of class.
Chapter 1.4: 10, 12, 16.
For 16, let the math courses be Algebra, Calculus, Geometry, and Counting and
let the professors be Smith, Jones, and Wang.
Chapter 1.5: 4, 8.
This page established September 14, 1998; last updated September 14, 1998.