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# Set notation

- Intro Lesson15:20
- Lesson: 16:33
- Lesson: 22:14
- Lesson: 3a1:26
- Lesson: 3b1:52
- Lesson: 3c0:59
- Lesson: 3d0:47
- Lesson: 3e1:44
- Lesson: 4a1:50
- Lesson: 4b0:53
- Lesson: 4c1:59
- Lesson: 4d2:14
- Lesson: 5a0:56
- Lesson: 5b1:28
- Lesson: 5c0:55
- Lesson: 5d0:42
- Lesson: 5e1:40
- Lesson: 5f0:21
- Lesson: 6a3:48
- Lesson: 6b0:30
- Lesson: 6c0:52

### Set notation

#### Lessons

In this lesson, we will learn:

- Drawing Venn Diagrams With Sets
- Understanding How to Use Set Notation
- Drawing and Interpreting Venn Diagrams

__Notes:__Here are some terms that we need to know for set notations:

__Set__: A list of objects or numbers.

__Element__: An object or a number in a set.

__n($A$)__: The number of elements in set $A$.

__Subset__: A set where all its elements belong to another set.

__Universal Set__: A set of all elements in a particular context.

__Empty Set__: A set with **no** elements.

__Disjoint__: Two or more sets that do not have any elements in common.

__Mutually Exclusive__: Two or more events that cannot happen simultaneously.

__Finite Set__: A set with a finite number of elements.

__Infinite Set__: A set with an infinite number of elements.

__Complement__: The list of remaining elements in the universal set that is not in the mentioned set. If $B$ is a set. Then we defined the complement to be $B'$ or $\overline{B}$.

- Introduction
__Set Notations Overview: Definitions and Terms__ - 1.
**Drawing Venn Diagrams With Sets**

Consider the following information:

- $A$ = {1, 2, 3}
- $B$ = {3, 4, 5}
- Universal Set $U$ = {1, 2, 3, 4, 5, 6, 7}

Draw a Venn Diagram describing the 3 sets.

- 2.
Consider the following information:

- $A$ = {1, 2, 3}
- $B$ = {4, 5, 6}
- Universal Set $U$ = {1, 2, 3, 4, 5, 6, 7}

Draw a Venn Diagram describing the 3 sets.

- 3.
**Understanding How to Use Set Notation**

Consider the following information:- Universal set $U$ = {0, 1, 2, 3, 4, 5,...}
- Set $N$ = {all natural numbers}
- Set $A$ = {0}
- Set $B$ = { }

a)Is set $N$ a finite set or an infinite set? What about set $B$ ?b)List all disjoint sets, if any.c)Determine $n(N)$ , $n(A)$ if possible.d)Patsy made a statement saying that $n(A)=n(B)$ . Is this true?e)Is the statement $N \subset U$ true? - 4.Consider the following Venn Diagram:
- Universal set $U = \{\mathrm{archery, eating, chess, darts,soccer, basketball, football, volleyball, tennis, badminton}\}$
- Set $A = \{\mathrm{archery, eating, chess, darts}\}$
- Set $B = \{\mathrm{soccer, basketball, football, volleyball}\}$

a)Explain what the sets $A,B$ and $U$ represent.b)List all disjoint sets, if any.c)List all the elements of $B'$ .d)Show that $n(A)+n(A')=n(U)$ . - 5.Consider the following Venn Diagram:a)What is the universal set?b)List all the elements in set $A$ and $B$.c)Find a subset for set $B$.d)List all disjoint sets, if any.e)Find $n(A)$, $n(B)$, and $n(C)$.f)Is set $C$ a finite set?
- 6.
**Drawing and Interpreting Venn Diagrams**Consider the following information:

- Universal Set $U =$ $\mathrm\{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$
- Set $A$ = {positive odd number up to 10}
- Set $B$ = {positive even number up to 10}
- Set $C$ = {0}

a)Draw a Venn diagramb)List all disjoint sets, if any.c)Find $n(A)$, $n(B)$, and $n(C)$.