Set Theory
1
, Learning Objectives
To learn and understand:
• concept of set, set membership, subset, set equality
• fundamental laws of set operations
• Cartesian product of two sets
• Venn diagram
• some special topics – Partition, Power set
• application of set theory
2
, Set Theory - Definitions and notations
• A set is a collection of well-defined items referred to as elements. A set is
said to contain its elements.
• Different ways of describing a set
Roster Method: listing the elements of a set
• {1, 2, 3} is the set containing “1”, “2” and “3” - list the members between
braces.
• {1, 1, 2, 3, 3} = {1, 2, 3} - since repetition is irrelevant
• {1, 2, 3} = {3, 2, 1} - since sets are unordered
• {1,2,3, …, 99} - is the set of positive integers <100
[use ellipses when the general pattern of the elements is obvious]
• {1, 2, 3, …} - is a way we denote an infinite set
[in this case, the natural numbers]
3
1
, Learning Objectives
To learn and understand:
• concept of set, set membership, subset, set equality
• fundamental laws of set operations
• Cartesian product of two sets
• Venn diagram
• some special topics – Partition, Power set
• application of set theory
2
, Set Theory - Definitions and notations
• A set is a collection of well-defined items referred to as elements. A set is
said to contain its elements.
• Different ways of describing a set
Roster Method: listing the elements of a set
• {1, 2, 3} is the set containing “1”, “2” and “3” - list the members between
braces.
• {1, 1, 2, 3, 3} = {1, 2, 3} - since repetition is irrelevant
• {1, 2, 3} = {3, 2, 1} - since sets are unordered
• {1,2,3, …, 99} - is the set of positive integers <100
[use ellipses when the general pattern of the elements is obvious]
• {1, 2, 3, …} - is a way we denote an infinite set
[in this case, the natural numbers]
3
