MAT 2720 Discrete Mathematics Section 1 1 Sets

MAT 2720 Discrete Mathematics Section 1. 1 Sets

Review? l You should have seen some of the basics of set theory.

Sets l Set : a collection of distinct unordered objects l Members of a set are called elements

Example 1

Set Builder Notation

Example 2

Special Sets l l The empty set has no elements. The universal set U: the set of all elements about which we make assertions.

Example 3 l Context: Number of solutions of a quadratic equations l Context: Stuff in your pocket

Cardinality l Cardinality of a set is the number of elements in the set

Subset l l l X is a subset of Y if every element of X is also contained in Y. X is a subset of Y if X is a sub-collection of elements in Y. Notation:

Example 4

Observation l is a subset of every set

Equality l Two sets X, Y are equal if and only if

Set Operations: Union The union of X and Y is defined as the set

Set Operations: Union The union of X and Y is defined as the set

Set Operations: Intersection The intersection of X and Y is defined as the set

Set Operations: Intersection The intersection of X and Y is defined as the set

Set Operations: Difference The difference of X and Y is defined as the set

Set Operations: Difference The difference of X and Y is defined as the set

Set Operations: Complement The complement of X is defined as the set

Set Operations: Complement The complement of X is defined as the set

Properties l Associative Laws l Commutative Laws

Properties l De Morgan’s Laws l Read all of these and more on this section.