Set Theory Basics

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