Sets and elements of sets

## 1. Summary of theory Tóm

### 1.1. Define:

– A collection of one or more objects with similar characteristics. Objects are called elements.

**VD:**

– Gather the students of grade 61

– The set of natural numbers that are multiples of 10 and less than 100

– Set of letters a, b, c, d

### 1.2. How to write symbols:

– The collection name is set with a capital letter.

**VD: **

A= { 0; first; 2; 3 }

B= { a; b; c; d }

C= { x \(\print\) N/ x<10}

– Elements are written in two {}

– Between elements are separated by “,” or “;”

– Arbitrary order of enumeration elements

– Each element is enumerated once

– There are two ways to write a set: List the elements of the set or show the characteristic properties of the elements.

**VD: **Write the set A of natural numbers that leave a remainder of 1 when divided by 2 and less than 10

A={1,3,5,6,7}

A= {x \(\print\) N/ x=2k+1; x<10}

**Symbol: **

a \(\print\) A reads a as an element of the set A or the element a in the set A.

a \(\notin\) A reads that a is not an element of the set A or the element a is not of the set A.

– A set can have one element, have many elements, have infinitely many elements, or have no element as an empty set. \(\emptyset\).

– If every element of set A belongs to set B, then set A is called a subset of set B. Symbol: A \(\subset\) B reads as: A is a subset of the set B, or A is contained in B, or B contains A.

Every set is a subset of itself, and the empty set is a subset of every set.

* How to find the number of subsets of a set: If A has n elements, then the number of subsets of A is 2n.

## 2. Illustrated exercise

**Question 1: **Let the set A be the letters in the phrase “Ho Chi Minh City”

a. List the elements of set A.

b. Fill in the appropriate symbol in the box

t [ ] A; c [ ] A; H [ ] A

**Solution guide:**

a/ A = {a, c, h, i, m, n, cell, p, t}

b/ b \(\notin\) A ; c \(\print\) A; H\(\print\) A

**HS Note: **The above problem does not distinguish between uppercase and lowercase letters in the given phrase.

**Verse 2: **Given the set of letters X = {A, C, O}

a/ Find the word phrase made up of the letters of the set X.

b/ Write the set X by showing the characteristic properties for the elements of X.

**Solution guide:**

a/ For example, the phrase “CAO CAO”

b/ X = {x: x-letter in the phrase “CAO CAO”}

**Question 3: **Let the set A = {1; 2;3;x; a; b}

a/ Specify the subsets of A that have 1 element.

b/ Specify the subsets of A that have 2 elements.

c/ Is the set B = {a, b, c} a subset of A?

**Solution guide:**

a/ {1} { 2} { a } { b} ….

b/ {1; 2} {1; a} {1; b} {2; a} {2; father; b} ……

c/ Set B is not a subset of set A because set B has element c but element c is not in set A.

**Question 4:** Let the set B = {a, b, c}. How many subsets does set B have in all?

**Solution guide:**

– The subset of B that has no word part is 1: \(\emptyset\)

– The subsets of B with one element are 3: {a}, {b}, {c}

– The subsets of B with two elements are 3: {a,b}, {a,c}, {b,c}

– The subset of B has 3 main elements: 1: {a, b, c}

So set A has all 1+3+3+1 = 8 subsets = 23

Note: Any set A always has two special subsets, the empty set and the set A itself. If A has n elements, the number of subsets of A is 2n.

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Let the set A be the letters in the phrase “Arithmetic Math 6”

a. List the elements of set A.

b. Fill in the appropriate symbol in the box

o [ ] A; a [ ] A; b [ ] A

**Verse 2: **Let the set A = {10; 20,30;x; y; z}

a/ Specify the subsets of A that have 1 element.

b/ Specify the subsets of A that have 2 elements.

c/ Is the set B = {x, y, z} a subset of A?

**Question 3:** Let the set B = {x, y, z, t}. How many subsets does set B have in all?

### 3.2. Multiple choice exercises Bài

**Question 1: **The number before 11 is:

A. 10

B. 9

C. 11

D. 12

**Verse 2: **How many elements are in the set of natural numbers not exceeding 5?

A. 4 elements

B. 5 elements

C. 6 elements

D. 7 elements

**Question 3: **How many elements does the set of elements in the sentence “GET247” include?

A. 4 elements

B. 5 elements

C. 6 elements

D. 7 elements

**Question 4: **The number following the number 77 is:

A. 80

B. 79

C. 77

D. 78

**Question 5: **The number that needs to be filled with the “…” sign in order to have an increasing dimension of less than 3 units is:

35,…,…

A. 32;29

B. 38;41

C. 34;33

D. 36;37

**Question 6: **How is the set E of natural numbers greater than 7 and less than 12 represented? Choose a correct option:

A. E = {8 ; 9 ; ten ; 11 ; twelfth}

B. E = {8 ; 9 ; ten ; 11}

C. E = {7 ; 8 ; 9 ; ten ; 11}

D. E = {7 ; 8 ; 9 ; ten ; 11}

**Verse 7: **Given two sets \(B = \left\{ {a;b} \right\};P = \left\{ {b;x;y} \right\}\). Choose the wrong comment

A. \(b \in B\)

B. \(x \in B\)

C. \(a \notin P\)

D. \(y \in P\)

**Verse 8: **Let the set B = {17; 19; 20; 21; 23}. Choose the correct answer

A. \(15 \in B\)

B. \(23 \in B\)

C. \(19 \notin B\)

D. \(15 \in B\) and \(23 \in B\)

**Verse 9: **The set S of the months of the fourth quarter of the year is

A. S = {July, August, September}

B.S = {April, May, June}

C. S = {January, February, March}

D. S= {October, November, December}

**Question 10: **The set of letters contained in the word “VUI HOC 247” is

A. A = {V; U; I; H; O; C}

B. A = {V; U; I; H; O; C; 2; 4; 7}

C. A = {V; U; I;2; 4; 7}

D. A = {V; U; I; H; O; 2; 4}

## 4. Conclusion

Through the lesson Collections and elements of this set, you need to accomplish some of the objectives given by the lesson, such as:

- Statement that defines the set, the element of the set.
- How to write symbols.
- How to list elements in a set.

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