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Set notation

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Intros
Lessons
  1. Set Notations Overview: Definitions and Terms
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Examples
Lessons
  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.

    1. 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.

      1. 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 = { }
        1. Is set NN a finite set or an infinite set? What about set BB ?
        2. List all disjoint sets, if any.
        3. Determine n(N)n(N) , n(A)n(A) if possible.
        4. Patsy made a statement saying that n(A)=n(B)n(A)=n(B) . Is this true?
        5. Is the statement N⊂UN \subset U true?
      2. 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}\}
        1. Explain what the sets A,BA,B and UU represent.
        2. List all disjoint sets, if any.
        3. List all the elements of B′B' .
        4. Show that n(A)+n(A′)=n(U)n(A)+n(A')=n(U) .
      3. Consider the following Venn Diagram:

        Consider the Venn Diagram

        1. What is the universal set?
        2. List all the elements in set AA and BB.
        3. Find a subset for set BB.
        4. List all disjoint sets, if any.
        5. Find n(A)n(A), n(B)n(B), and n(C)n(C).
        6. Is set CC a finite set?
      4. 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}
        1. Draw a Venn diagram
        2. List all disjoint sets, if any.
        3. Find n(A)n(A), n(B)n(B), and n(C)n(C).
      Topic Notes
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      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 B′B' or B‾\overline{B}.