Set notation

Set notation

Lessons

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}.

  • 1.
    Introduction to Set Notation: Definitions and Terms

  • 2.
    Drawing Venn Diagrams With Sets

    Consider the following information:

    - A=A = {1,2,31, 2, 3}

    - B=B= {3,4,53, 4, 5}

    - Universal Set UU = {1,2,3,4,5,6,71, 2, 3, 4, 5, 6, 7}

    Draw a Venn Diagram describing the 3 sets.


  • 3.
    Consider the following information:

    - AA = {1,2,31, 2, 3}

    - BB = {4,5,64, 5, 6}

    - Universal Set UU = {1,2,3,4,5,6,71, 2, 3, 4, 5, 6, 7}

    Draw a Venn Diagram describing the 3 sets.


  • 4.
    Understanding How to Use Set Notation

    Consider the following information:

    - Universal set UU = {0,1,2,3,4,5,...0, 1, 2, 3, 4, 5, ...}

    - Set NN = {all natural numbers}

    - Set AA = {00}

    - 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(A) if possible.

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

    e)
    Is the statement N \subset U true?


  • 5.
    Consider the following Venn Diagram:

    - Universal set U=U = {archery, eating, chess, darts, soccer, basketball, football, volleyball, badminton}

    - Set A=A = {archery, eating, chess, darts}

    - Set B=B = {soccer, basketball, football, volleyball}

    a)
    Explain what the sets A and B represent.

    b)
    List all disjoint sets, if any.

    c)
    List all the elements of BB'.

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


  • 6.
    Consider the following Venn Diagram:

    Consider the Venn Diagram

    a)
    What is the universal set?

    b)
    List all the elements in set A and B.

    c)
    Find a subset for set B.

    d)
    List all disjoint sets, if any.

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

    f)
    Is set C a finite set?


  • 7.
    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}

    - Set A = {positive odd number up to 10}

    - Set B = {positive even number up to 10}

    - Set C = {0}

    a)
    Draw a Venn diagram

    b)
    List all disjoint sets, if any.

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