1. Basic Concepts of Sets

• Set: A well-defined collection of distinct objects (called elements or members).

  Example: A = {1, 2, 5, a, △}

• Notation: Use curly braces {}.

  Example: {x | x is an even number

• Element Membership:

  • x ∈ A means x is in A
  • x ∉ A means x is not in A

• Cardinality (Size):

  • Denoted by |A|, the number of distinct elements.
  • Example: |A| = 5 for A = {1, 2, 5, a, △}

2. Operations on Sets (Set Algebra)

a. Union: A ∪ B

• All elements in A, B, or both.

• Notation: {x | x ∈ A or x ∈ B}

• Example:

  A = {1, 2, 5, a, △},

  B = {3, a, △, 7}

  ⇒ A ∪ B = {1, 2, 5, a, △, 3, 7}

b. Intersection: A ∩ B

• Only elements common to both A and B.
• Notation: {x | x ∈ A and x ∈ B}
• Example: A ∩ B = {a, △}

c. Difference: A \ B or A – B

• Elements in A but not in B.
• Notation: {x ∈ A | x ∉ B}

d. Complement: Aᶜ

• Elements in the universal set U not in A.
• Notation: {x ∈ U | x ∉ A}