129
Sets and subsets
Textbook: Part 4, lesson 129, pp. 60–62
GoalEqual sets, the number of elements, the empty set; picking a part of a set.
New words
equal sets · teng to‘plamlarempty set · bo‘sh to‘plamnumber of elements · elementlar sonisubset · qismto‘plam
Explanation
Two sets are equal if they consist of the same elements: A = B. The order in which the elements are written does not matter. In a set each element is counted only once. A set with no elements is called the empty set and is written ∅. If we pick some elements of a set, we get a new set – a subset.
Worked examples
A = {2, 4, 6} and B = {6, 2, 4} have the same elements, so A = B. In C = {1, 2, 3} and D = {1, 2, 3, 4}, D has 4 and C does not, so C ≠ D.
The set of letters of “papa” is {p, a} – 2 elements (repeated letters are counted once). The set of one-digit numbers greater than 100 is empty: ∅.
Class activity
“Equal or not?”: two groups hold cards with the same elements written in different orders. The class compares the cards and answers “A = B” or “A ≠ B”.
Practice
1
How many elements does the set of letters of the word “kitob” have?
5
2
Write the set of multiples of 10 from 20 to 40 (20 and 40 included).
{20, 30, 40}
3
A = {5, 7, 9} and B = {9, 5, 7}. Are these sets equal?
Yes, A = B (the order does not matter).
4
Write the set of natural numbers that are less than 7 and greater than 9.
There is no such number; it is the empty set: ∅.
5
From A = {1, 2, 3, 4, 5, 6} make the subset B of even numbers. How many elements does it have?
B = {2, 4, 6}, 3 elements