Functions

Ordered Pair & Cartesian Product

Ordered Pair

An ordered pair is a pair of elements written in a specific order. An ordered pair is written as (a, b) where:

• a = first element
• b = second element

Important Rule: \((a, b) \neq (b, a) \text{ unless } a = b\)

Cartesian Product

The Cartesian product of two sets A and B is the set of all ordered pairs (a, b), where: a ∈ A and b ∈ B

Notation: \(A \times B = {(a, b) : a \in A, b \in B}\)

Example: If A = {1, 2} B = {x, y} Then \(A \times B = {(1,x), (1,y), (2,x), (2,y)}\)

Key Points: Order matters ( A \times B \neq B \times A )

Function

A function is a relation in which each element of a set (domain) is mapped to exactly one element of another set (codomain).

Notation: \(f: A \to B \)

👉 This means: A = Domain  B = Codomain

👉 Example: \(f(x) = x^2\) If input is 2 → output is 4