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MCQ Practice
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