Tashkent university of information technologies named after muhammad al-khorazmi, ministry of information technology and communication development of the republic of uzbekistan discrete structure science topic: mi3 Cartesian multiplication of

TASHKENT UNIVERSITY OF INFORMATION TECHNOLOGIES NAMED AFTER MUHAMMAD AL-KHORAZMI, MINISTRY OF INFORMATION TECHNOLOGY AND COMMUNICATION DEVELOPMENT OF THE REPUBLIC OF UZBEKISTAN Discrete structure science topic: MI3 Cartesian multiplication of sets, relations given in the Cartesian square, methods and properties Full Name: Abdumutalibov Odilbek group number:214-21

Example: Let A = {a, b, c} and B = {p,q}.

• Example: Let A = {a, b, c} and B = {p,q}.
• Then A × B = {(a, p), (a, q), (b, p),(b, q), (c, p), (c, q)}
• Also B × A = {(p, a), (p, b), (p, c), (q, a), (q, b), (q, c)}

Cartesian Product
The cartesian product of two or more sets is the set of all ordered pairs/n-tuples of the sets. It is most commonly implemented in set theory. In addition to this, many real-life objects can be represented by using cartesian products such as a deck of cards, chess boards, computer images, etc. Most of the digital images displayed by computers are represented as pixels which are graphical representations of cartesian products.
In this article, let's learn about the cartesian product, its properties, and the product of sets with solved examples for a better understanding. We will discuss the cartesian product of two or more sets and relations.
What Is a Cartesian Product?
Cartesian product is the product of any two sets, but this product is actually ordered i.e, the resultant set contains all possible and ordered pairs such that the first element of the pair belongs to the first set and the second element belongs to the second set. Since their order of appearance is important, we call them first and second elements, respectively. We use ordered pairs to obtain a new set from two given sets A and B.

An ordered pair (p, q) consists of two values p and q. Example: (1, 3) and (- 4, 10) are ordered pairs where these pairs of numbers are in a specific order.

• An ordered pair (p, q) consists of two values p and q. Example: (1, 3) and (- 4, 10) are ordered pairs where these pairs of numbers are in a specific order.
• Consequently, (p, q) ≠ (q,p) unless p = q. In general, (p, q) = (s, t) if and only if p = s and q = t. Example: (1, 3) is not equivalent to (3, 1) i.e., (1, 3) ≠ (3, 1).
• An ordered pair is a pair of numbers in a specific order. For example, (1, 2) and (- 4, 12) are ordered pairs. The order of the two numbers is important: (1, 2) is not equivalent to (2, 1) -- (1, 2)≠(2, 1).