Download presentation

Presentation is loading. Please wait.

Published byMiranda Marianna Small Modified over 4 years ago

1
2.1 – Symbols and Terminology Definitions: Set: A collection of objects. Elements: The objects that belong to the set. Set Designations (3 types): Word Descriptions: The set of even counting numbers less than ten. Listing method: {2, 4, 6, 8} Set Builder Notation: {x | x is an even counting number less than 10}

2
2.1 – Symbols and Terminology Definitions: Empty Set: A set that contains no elements. It is also known as the Null Set. The symbol is List all the elements of the following sets. The set of counting numbers between six and thirteen. {7, 8, 9, 10, 11, 12} {5, 6, 7,…., 13} {x | x is a counting number between 6 and 7} {5, 6, 7, 8, 9, 10, 11, 12, 13} Empty set Null set { }

3
2.1 – Symbols and Terminology Symbols: ∈ : Used to replace the words “is an element of.” 3 ∈ {1, 2, 5, 9, 13} False 0 ∈ {0, 1, 2, 3} -5 ∉ {5, 10, 15, , } True ∉ : Used to replace the words “is not an element of.” True or False: True

4
2.1 – Symbols and Terminology Sets of Numbers and Cardinality n(A): n of A; represents the cardinal number of a set. K = {2, 4, 8, 16} n(K) = 4 ∅ R = {1, 2, 3, 2, 4, 5} n(R) = 5 n( ∅ ) = 0 Cardinal Number or Cardinality: The number of distinct elements in a set. Notation P = { ∅ } n(P) = 1

5
2.1 – Symbols and Terminology Finite and Infinite Sets {2, 4, 8, 16}Countable = Finite set {1, 2, 3, …} Not countable = Infinite set Finite set: The number of elements in a set are countable. Infinite set: The number of elements in a set are not countable

6
2.1 – Symbols and Terminology Equality of Sets {–4, 3, 2, 5} and {–4, 0, 3, 2, 5} Are the following sets equal? Equal Not equal Set A is equal to set B if the following conditions are met: 1. Every element of A is an element of B. 2. Every element of B is an element of A. {3} = {x | x is a counting number between 2 and 5} Not equal {11, 12, 13,…} = {x | x is a natural number greater than 10}

7
2.2 – Venn Diagrams and Subsets Definitions: Universal set: the set that contains every object of interest in the universe. Complement of a Set: A set of objects of the universal set that are not an element of a set inside the universal set. Notation: A U A A Venn Diagram: A rectangle represents the universal set and circles represent sets of interest within the universal set

8
2.2 – Venn Diagrams and Subsets Definitions: Subset of a Set: Set A is a Subset of B if every element of A is an element of B. Notation: A B {3, 4, 5, 6} {3, 4, 5, 6, 8} BBBB Subset or not? Note: Every set is a subset of itself. {1, 2, 6} {2, 4, 6, 8} {5, 6, 7, 8}

9
2.2 – Venn Diagrams and Subsets Definitions: Set Equality: Given A and B are sets, then A = B if A B and B A. {1, 2, 6} = {5, 6, 7, 8} {5, 6, 7, 8, 9}

10
2.2 – Venn Diagrams and Subsets Definitions: The empty set ( ) is a subset and a proper subset of every set except itself. Proper Subset of a Set: Set A is a proper subset of Set B if A B and A B. Notation A B {3, 4, 5, 6} {3, 4, 5, 6, 8} both {1, 2, 6} {1, 2, 4, 6, 8} both {5, 6, 7, 8} What makes the following statements true? , , or both

11
2.2 – Venn Diagrams and Subsets Number of Subsets The number of subsets of a set with n elements is: 2 n {1} List the subsets and proper subsets Number of Proper Subsets The number of proper subsets of a set with n elements is: 2 n – 1 {1, 2} {2} {1,2} {1} {2} Subsets: Proper subsets: 2 2 = 4 2 2 – 1= 3

12
2.2 – Venn Diagrams and Subsets {a} List the subsets and proper subsets {a, b, c} {b} {c} {a, b}{a, c} Subsets: Proper subsets: 2 3 = 8 2 3 – 1 = 7 {b, c} {a, b, c} {a} {b} {c} {a, b}{a, c}{b, c}

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google