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# Set notation

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### Set notation

#### Lessons

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 $\overline{B}$.

- 1.
__Introduction to Set Notation: Definitions and Terms__ - 2.
**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.

- 3.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.

- 4.
**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? - 5.Consider the following Venn Diagram:
- Universal set $U =$ {archery, eating, chess, darts, soccer, basketball, football, volleyball, badminton}

- Set $A =$ {archery, eating, chess, darts}

- Set $B =$ {soccer, basketball, football, volleyball}

a)Explain what the sets A and B represent.b)List all disjoint sets, if any.c)List all the elements of $B'$.d)Show that n(A) + n(A') = n(U). - 6.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?
- 7.
**Drawing and Interpreting Venn Diagrams**Consider the following information:

- Universal Set $U =$ {-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).