Sets

A set is a well

A set is a well-defined collection of distinct objects. Example: A = {2, 4, 6, 8} (roster form) or A = {x : x is an even natural number less than 10}

Empty Set (∅)

Empty Set (∅): Contains no elements. Example: {x : x² = -1, x ∈ R}. Finite Set: Contains countable elements. Example: {1, 2, 3, 4, 5}. Infinite Set: C

Set A is a subset

Set A is a subset of B (A ⊆ B) if every element of A belongs to B. Problem-solving steps: 1) List all elements of both sets, 2) Check if each element

Union (A ∪ B)

Union (A ∪ B): All elements in A or B or both. Step-by-step: 1) List all elements from A, 2) Add elements from B that aren't already listed, 3) Write

Difference (A

Difference (A - B): Elements in A but not in B. Method: 1) Take each element of A, 2) Check if it's in B, 3) If not, include it in A - B. Example: A =