Sets and Relations

A set is a well

A set is a well-defined collection of distinct objects. Example: A = {1, 2, 3, 4} (Roster method) or A = {x | x ∈ N, x ≤ 4} (Set-Builder method). The

Empty set (φ)

Empty set (φ): Contains no elements, n(φ) = 0. Singleton set: Contains exactly one element, like {5}. Finite set: Has countable elements. Infinite set

Union (A ∪ B)

Union (A ∪ B): All elements in A or B. Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}. Intersection (A ∩ B): Common element

Two fundamental laws

Two fundamental laws: (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'. Example verification: Let U = {1, 2, 3, 4, 5}, A = {1, 2, 3}, B = {3, 4, 5}. Then A ∪

Represent continuous sets of real numbers

Represent continuous sets of real numbers. Open interval (a, b) = {x | a < x < b}, excludes endpoints. Closed interval [a, b] = {x | a ≤ x ≤ b}, inclu