# 1. Objective / Мета роботи

**Understand and implement the Cartesian product of sets and the related
operations on binary relations.**

By the end of the work the student should be able to:

- **construct the Cartesian product** $A \times B$ of two finite sets as the set
  of all **ordered pairs** $(a, b)$ with $a \in A$ and $b \in B$, using only
  basic data structures;
- explain a **binary relation** as a **subset** of $A \times B$, and **validate**
  whether a given list of ordered pairs is a legitimate relation for two sets;
- **generate a relation** on a set from a **predicate** (relation function), such
  as a divisibility rule;
- **filter** a Cartesian product to the pairs that satisfy a supplied condition;
- reason about the **size** of a product ($|A \times B| = |A|\cdot|B|$) and about
  the **time complexity** of each operation.

The work builds directly on the set operations of Laboratory Work 1 and prepares
the ground for the study of relations, functions, and graphs later in the course.