## Math 6 Chapter 1 Lesson 4: Number of elements of a set and subsets

## 1. Summary of theory Tóm

### 1.1. The number of elements of a set

For the following sets:

\(\begin{array}{l} A = \left\{ 5 \right\}\\ B = \left\{ {x;y} \right\}\\ C = \left\{ {1;2 ;3;…;100} \right\}\\ N = \left\{ {0;1;2;…} \right\} \end{array}\)

We say that set A has one element, set B has two elements, set C has 100 elements, and set N has infinitely many elements.

**Attention:**

The set with no elements is called the empty set

The empty set is denoted by . \(\emptyset \)

A set can have one element, many elements, an infinite number of elements, or no elements at all.

### 1.2. Subset

\(\begin{array}{l} E = \left\{ {x,y} \right\},\\ F = \left\{ {x,y,c,d} \right\} \end{ array}\)

**Comment:**

If every element of set A belongs to set B, then set A is said to be a subset of set B.

I sign \(A \subset B\) nice \(B \supset A\)

Read as A is a subset of the set B, or A is contained in B, or B contains A.

If \(A \subset B\) and \(B \subset A\) then we say that A and B are two equal sets, denoted by \(A = B\)

## 2. Illustrated exercise

**Question 1: **Find the subsets of set A in the following cases:

a) A has only one element \(A = \left\{ a \right\}\)

b) A has two elements \(A = \left\{ {a;b} \right\}\)

c) A has 3 elements \(A = \left\{ {a,b,c} \right\}\)

d) General: If A has n elements, how many subsets are there?

**Solution guide:**

a) The set \(A = \left\{ a \right\}\) has two subsets \(\left\{ a \right\},\emptyset \)

b) The set \(A = \left\{ {a;b} \right\}\) has four subsets \(\left\{ a \right\},\left\{ b \right\},\ left\{ {a,b} \right\}\emptyset \)

c) The set \(A = \left\{ {a,b,c} \right\}\) has 8 subsets \(\left\{ a \right\},\left\{ b \right\} ,\left\{ c \right\},\left\{ {a,b} \right\},\left\{ {a,c} \right\},\left\{ {b,c} \right \},A,\emptyset \)

d) If A has n elements, then there are 2x2x2x…x2 (n times) subsets

**Verse 2: **Let A be the set of natural numbers greater than 3 and less than 8. Write the set in 2 ways (list and describe it)

**Solution guide:**

* Method 1: Write A by listing the element: \(A = \left\{ {4;5;6;7} \right\}\)

* Method 2: Write A by stating the characteristic \(A = \left\{ {n \in N|3 < n < 8} \right\}\)

## 3. Practice

### 3.1. Essay exercises

**Question 1:**

a) Find a subset of a set A with 3 elements \(A = \left\{ {x, y, z} \right\}\)

d) A has 20 elements, how many subsets does it have?

**Verse 2: **Let A be the set of even natural numbers greater than 10 and less than 25. Write the set in two ways (list and describe it)

### 3.2. Multiple choice exercises Bài

**Question 1: **Given the set \(A = \left\{ {0;2;4;6} \right\}\), how many elements does A have:

A. 1

B. 2

C. 3

D. 4

**Verse 2: **How many elements does the set \(B = \left\{ {6;7;8;…;56} \right\}\) have?

A. 56

B. 54

C. 51

D. 50

**Question 3: **Given the set \(A = \left\{ {1;3;4;5;8} \right\}\), the subset of A is:

A. \(B = \left\{ {0;3;4;5;8} \right\}\)

B. \(C = \left\{ {2;4;5;8} \right\}\)

C. \(D = \left\{ {1;4;5;8;9} \right\}\)

D. \(E = \emptyset \)

**Question 4: **Find the natural number x such that x + 6 = 4

A. x = 0

B. x = 1

C. \(x = \left\{ \emptyset \right\}\)

D. x = 4

**Question 5: **Given two sets \(A = \left\{ {0;2;4} \right\},B = \left\{ {0;1;2;3;4;5} \right\}\). Which of the following statements false:

A. Set A has 3 elements

B. Set A is a subset of set B

C. The set A is contained in the set B

D. The set A is equal to the set B

## 4. Conclusion

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

- What is a subset?
- The number of elements of a set.

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