Set Operations: Union and Intersection

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.