Set Operations: Union and Intersection
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Questions and Answers

What is the formula for the union of two sets A and B?

  • A ∪ B = {x | x ∉ A and x ∉ B}
  • A ∪ B = {x | x ∈ A or x ∈ B} (correct)
  • A ∪ B = {x | x ∈ A and x ∈ B}
  • A ∪ B = {x | x ∈ A - x ∈ B}

    • What is the intersection of sets A = {1, 2, 3} and B = {3, 4, 5}?

  • {1, 2}
  • {3} (correct)
  • {4, 5}
  • {1, 2, 3, 4, 5}

    • What is the difference of sets A = {1, 2, 3} and B = {3, 4, 5}?

  • {3}
  • {1, 2, 3, 4, 5}
  • {4, 5}
  • {1, 2} (correct)

    • Is the difference of sets A and B commutative?

    <p>No, A \ B ≠ B \ A in general</p> Signup and view all the answers

    What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?

    <p>{1, 2, 3, 4, 5}</p> Signup and view all the answers

    Study Notes

    Sets

    Union Of Sets

    • The union of two sets A and B, denoted as A ∪ B, is the set of all elements that are in A, in B, or in both.
    • Formula: A ∪ B = {x | x ∈ A or x ∈ B}
    • Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}

    Intersection Of Sets

    • The intersection of two sets A and B, denoted as A ∩ B, is the set of all elements that are common to both A and B.
    • Formula: A ∩ B = {x | x ∈ A and x ∈ B}
    • Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}

    Difference Of Sets

    • The difference of two sets A and B, denoted as A \ B, is the set of all elements that are in A but not in B.
    • Formula: A \ B = {x | x ∈ A and x ∉ B}
    • Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A \ B = {1, 2}
    • Note: The difference of sets is not commutative, i.e. A \ B ≠ B \ A in general.

    Sets

    Union of Sets

    • Union of two sets A and B, denoted as A ∪ B, contains all elements from A, B, or both.
    • Formula: A ∪ B = {x | x ∈ A or x ∈ B}
    • Example: A = {1, 2, 3} and B = {3, 4, 5} → A ∪ B = {1, 2, 3, 4, 5}

    Intersection of Sets

    • Intersection of two sets A and B, denoted as A ∩ B, contains all elements common to both A and B.
    • Formula: A ∩ B = {x | x ∈ A and x ∈ B}
    • Example: A = {1, 2, 3} and B = {3, 4, 5} → A ∩ B = {3}

    Difference of Sets

    • Difference of two sets A and B, denoted as A \ B, contains all elements in A but not in B.
    • Formula: A \ B = {x | x ∈ A and x ∉ B}
    • Example: A = {1, 2, 3} and B = {3, 4, 5} → A \ B = {1, 2}
    • Note: A \ B ≠ B \ A in general, as the difference of sets is not commutative.

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    Description

    Learn about the union and intersection of sets, including their formulas and examples. Understand how to find the union and intersection of two sets.

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