Concepts & Solved Examples
Learn ordered pair equality, Cartesian cross product $A \times B$, subset counts, and Examples 1 to 6.
Exercise 3.1 Solutions
Detailed step-by-step textbook solutions to all parts of Exercise 3.1 with interactive answer details.
Chapter Worksheets
Three levels (Easy, Medium, Hard) of worksheets targeting cross products and subset sizes.
Revision Notes
Ordered pair vs set comparison, properties table, subset counts, and common pitfalls.
Interactive Tests
Basic, Standard, and Advanced quizzes with 10 questions each to test your understanding of Cartesian products.
What You'll Learn in This Section
Welcome to Chapter 3! We start by establishing how connections are formed between mathematical objects. Before we define relations and functions, we need to understand **Ordered Pairs** (where order matters) and the **Cartesian Product of Sets** (the set of all possible ordered pairs between two sets).
- Ordered Pairs: $(a, b)$ is different from $(b, a)$ unless $a = b$. Two ordered pairs are equal if corresponding components are equal.
- Cartesian Product: $A \times B = \{(a, b) : a \in A \text{ and } b \in B\}$.
- Properties: Cardinality rule $n(A \times B) = n(A) \times n(B)$, distributive laws over union and intersection, and subset counts ($2^{n(A \times B)}$).
Start Learning
Click on Concepts & Solved Examples to begin studying the theory, or go straight to Exercise 3.1 Solutions to check your homework answers.