Sets and Their Operations
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Questions and Answers

What is a set?

  • A collection that contains at least one element
  • A random collection of items
  • A collection of definite and distinct objects (correct)
  • A collection that can be infinitely large

    • What is an empty set?

    The set that contains no elements.

    What are subsets?

    When every element of A is also an element of B.

    What are equal sets?

    <p>Sets that contain exactly the same members.</p> Signup and view all the answers

    What is a universal set?

    <p>The set of all possible elements from which subsets are formed.</p> Signup and view all the answers

    What is the complement of a set?

    <p>The set of all elements in the universal set that are not in a given set.</p> Signup and view all the answers

    What is the union of sets?

    <p>The set of elements in either A or B (or in both).</p> Signup and view all the answers

    What is the intersection of sets?

    <p>The set of elements that are in both A and B.</p> Signup and view all the answers

    What is a Venn diagram?

    <p>A diagram that uses circles to show comparison.</p> Signup and view all the answers

    What is a proper set?

    <p>Every element in a set is also an element in another set, and the sets are not equal.</p> Signup and view all the answers

    What is a singleton set?

    <p>A set with only one element.</p> Signup and view all the answers

    What is a power set?

    <p>Set of all subsets.</p> Signup and view all the answers

    What is the symmetric difference of two sets?

    <p>(A-B) U (B-A)</p> Signup and view all the answers

    What is the cardinal number of a set?

    <p>The number of distinct elements in a finite set.</p> Signup and view all the answers

    What are equivalent sets?

    <p>Two or more sets that have the same number of elements.</p> Signup and view all the answers

    Study Notes

    Sets

    • Developed by German mathematician George Cantor (1845-1918).
    • Fundamental in relations, functions, logic, and probability theory.
    • Defined as a collection of distinct objects or elements.

    Empty Set / Null Set

    • Defined as a set containing no elements.
    • Notated with open brackets: {}.

    Subsets

    • A set A is a subset of B if every element of A is also an element of B.

    Equal Sets

    • Two sets are equal if they contain exactly the same members.

    Universal Set

    • The universal set includes all possible elements from which subsets are derived.

    Complement of a Set

    • Refers to elements in the universal set that are not included in a specified set.

    Union of Sets

    • Union of sets A and B is denoted as A U B.
    • Includes all elements present in either set A or set B (or both).

    Intersection of Sets

    • Intersection of sets A and B is denoted as A ∩ B.
    • Contains all elements present in both sets A and B.

    Venn Diagram

    • A visual representation using circles to illustrate the relationships and comparisons between different sets.

    Proper Set

    • A set is a proper set if all its elements belong to another set, and they are not identical.

    Singleton Set

    • A set that consists of only one element.

    Power Set

    • The power set is the collection of all possible subsets of a given set.

    Symmetric Difference of Two Sets

    • Denoted as A∆B which represents (A - B) U (B - A).
    • It includes elements that are in either set A or set B but not in both.

    Cardinal Number of Sets

    • Refers to the number of distinct elements in a finite set, denoted as n(A).
    • Example: For A = {1, 2, 3, 4, 5}, n(A) = 5.

    Equivalent Sets

    • Two or more sets are equivalent if they contain the same number of elements.

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    Quiz Team

    Description

    This quiz covers the fundamental concepts of sets, including definitions, types of sets such as empty sets and subsets, and operations like union and intersection. Additionally, the importance of Venn diagrams for visual representation is highlighted. Test your understanding of these key mathematical principles.

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