Set Theory Basics
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Questions and Answers

What is the set of all elements that are in A, in B, or in both, denoted by?

  • A ∩ B
  • A ∪ B (correct)
  • A'
  • A × B

    • What is the set of all elements that are common to both A and B, denoted by?

  • A × B
  • A ∪ B
  • A'
  • A ∩ B (correct)

    • What is the set of all elements that are not in A, denoted by?

  • A × B
  • A' (correct)
  • A ∪ B
  • A ∩ B

    • What is a graphical representation of sets and their relationships?

    <p>Venn diagram</p> Signup and view all the answers

    What is the set of all ordered pairs (a, b) where a is in A and b is in B, denoted by?

    <p>A × B</p> Signup and view all the answers

    What is the universal set U in the example of the complement of a set A?

    <p>{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}</p> Signup and view all the answers

    What is a characteristic of the Straight-Line Method of depreciation?

    <p>It allocates the cost of an asset evenly over its useful life.</p> Signup and view all the answers

    What is the formula for calculating depreciation using the Straight-Line Method?

    <p>Depreciation = (Cost of Asset - Residual Value) / Useful Life</p> Signup and view all the answers

    What is the purpose of Accumulated Depreciation?

    <p>To decrease the value of an asset over time.</p> Signup and view all the answers

    Where is Accumulated Depreciation presented on the balance sheet?

    <p>As a contra-asset account.</p> Signup and view all the answers

    What is the result of dividing the Cost of Asset by the Useful Life?

    <p>Annual Depreciation Expense.</p> Signup and view all the answers

    What is the effect of Accumulated Depreciation on the asset's value?

    <p>It decreases the asset's value.</p> Signup and view all the answers

    Study Notes

    Set Theory

    Union

    • 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.
    • Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}

    Intersection

    • 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.
    • Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}

    Complement

    • The complement of a set A, denoted as A', is the set of all elements that are not in A.
    • Example: If A = {1, 2, 3} and the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then A' = {4, 5, 6, 7, 8, 9, 10}

    Venn Diagrams

    • A Venn diagram is a graphical representation of sets and their relationships.
    • It consists of overlapping circles, each representing a set.
    • The regions of the diagram can be labeled to indicate the intersection and union of the sets.

    Cartesian Product

    • The Cartesian product of two sets A and B, denoted as A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B.
    • Example: If A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}

    Set Theory

    Union of Sets

    • The union of two sets A and B, denoted as A ∪ B, combines all elements from both sets.
    • Example: A = {1, 2, 3} and B = {3, 4, 5} ⇒ A ∪ B = {1, 2, 3, 4, 5}

    Intersection of Sets

    • The intersection of two sets A and B, denoted as A ∩ B, consists of elements common to both sets.
    • Example: A = {1, 2, 3} and B = {3, 4, 5} ⇒ A ∩ B = {3}

    Complement of a Set

    • The complement of a set A, denoted as A', includes all elements not in A.
    • Example: A = {1, 2, 3} and universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ⇒ A' = {4, 5, 6, 7, 8, 9, 10}

    Venn Diagrams

    • Venn diagrams graphically represent sets and their relationships using overlapping circles.
    • Diagram regions can be labeled to show set intersections and unions.

    Cartesian Product

    • The Cartesian product of two sets A and B, denoted as A × B, combines elements from both sets as ordered pairs.
    • Example: A = {1, 2} and B = {3, 4} ⇒ A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}

    Depreciation

    Straight-Line Method

    • Allocates asset cost evenly over its useful life, assuming constant value loss over time
    • Ignores actual asset usage or productivity
    • Suitable for assets with long useful life and stable usage patterns

    Depreciation Formula

    • Depreciation = (Cost of Asset - Residual Value) / Useful Life
    • Cost of Asset: initial asset cost
    • Residual Value: estimated value at end of useful life
    • Useful Life: expected years of asset use

    Accumulated Depreciation

    • Total depreciation allocated to an asset over its useful life
    • Represents asset value decrease over time
    • Contra-asset account on balance sheet, reducing asset carrying value
    • Calculated by summing annual depreciation expenses over useful life

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    Description

    Learn about the fundamental concepts of set theory, including union, intersection, and complement. Test your understanding of these essential set operations.

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