Set notation

Set notation

Lessons

In this lesson, we will learn:

  • Drawing Venn Diagrams With Sets
  • Understanding How to Use Set Notation
  • Drawing and Interpreting Venn Diagrams

Notes:

Here are some terms that we need to know for set notations:

Set: A list of objects or numbers.

Element: An object or a number in a set.

n(AA): The number of elements in set AA.

Subset: A set where all its elements belong to another set.

Universal Set: A set of all elements in a particular context.

Empty Set: A set with no elements.

Disjoint: Two or more sets that do not have any elements in common.

Mutually Exclusive: Two or more events that cannot happen simultaneously.

Finite Set: A set with a finite number of elements.

Infinite Set: A set with an infinite number of elements.

Complement: The list of remaining elements in the universal set that is not in the mentioned set. If BB is a set. Then we defined the complement to be BB' or B\overline{B}.

  • Introduction
    Set Notations Overview: Definitions and Terms

  • 1.
    Drawing Venn Diagrams With Sets

    Consider the following information:

    • AA = {1, 2, 3}
    • BB = {3, 4, 5}
    • Universal Set UU = {1, 2, 3, 4, 5, 6, 7}

    Draw a Venn Diagram describing the 3 sets.


  • 2.

    Consider the following information:

    • AA = {1, 2, 3}
    • BB = {4, 5, 6}
    • Universal Set UU = {1, 2, 3, 4, 5, 6, 7}

    Draw a Venn Diagram describing the 3 sets.


  • 3.
    Understanding How to Use Set Notation
    Consider the following information:
    • Universal set UU = {0, 1, 2, 3, 4, 5,...}
    • Set NN = {all natural numbers}
    • Set AA = {0}
    • Set BB = { }
    a)
    Is set NN a finite set or an infinite set? What about set BB ?

    b)
    List all disjoint sets, if any.

    c)
    Determine n(N)n(N) , n(A)n(A) if possible.

    d)
    Patsy made a statement saying that n(A)=n(B)n(A)=n(B) . Is this true?

    e)
    Is the statement NUN \subset U true?


  • 4.
    Consider the following Venn Diagram:
    • Universal set U={archery,eating,chess,darts,soccer,basketball,football,volleyball,tennis,badminton}U = \{\mathrm{archery, eating, chess, darts,soccer, basketball, football, volleyball, tennis, badminton}\}
    • Set A={archery,eating,chess,darts}A = \{\mathrm{archery, eating, chess, darts}\}
    • Set B={soccer,basketball,football,volleyball}B = \{\mathrm{soccer, basketball, football, volleyball}\}
    a)
    Explain what the sets A,BA,B and UU represent.

    b)
    List all disjoint sets, if any.

    c)
    List all the elements of BB' .

    d)
    Show that n(A)+n(A)=n(U)n(A)+n(A')=n(U) .


  • 5.
    Consider the following Venn Diagram:

    Consider the Venn Diagram

    a)
    What is the universal set?

    b)
    List all the elements in set AA and BB.

    c)
    Find a subset for set BB.

    d)
    List all disjoint sets, if any.

    e)
    Find n(A)n(A), n(B)n(B), and n(C)n(C).

    f)
    Is set CC a finite set?


  • 6.
    Drawing and Interpreting Venn Diagrams

    Consider the following information:

    • Universal Set U=U = {10,9,8,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,8,9,10}\mathrm\{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
    • Set AA = {positive odd number up to 10}
    • Set BB = {positive even number up to 10}
    • Set CC = {0}
    a)
    Draw a Venn diagram

    b)
    List all disjoint sets, if any.

    c)
    Find n(A)n(A), n(B)n(B), and n(C)n(C).