23.01 Set notation and Venn diagrams

List all the possible outcomes when a coin is flipped.

A standard six-sided die is rolled.

List all the elements in the following sets:

Consider the following sets:

A = \left\{1, 2, 4, 8, 16\right\}, \quad B = \left\{1, 2, 4, 8\right\}

List all the elements in:

Consider the set A = \left\{2, 4, 6, 8\right\}. Construct set builder notation for A.

Consider the following sets:

A = \left\{8, 12, 16, 20, 24, 28\right\}, B = \left\{8, 12, 16, 28\right\}, C = \left\{12, 16\right\}, \text{and } D = \left\{4, 8, 12, 16, 20, 24, 28\right\}

Determine whether the following statements are true or false:

Write \subseteq or \nsubseteq to make each of the following statements true:

Write \in or \notin to make each of the following statements true:

Consider the following sets:

• A= \{ \text{letters of the word `parallelogram'}\}
• B= \{ \text{letters of the word `gallop'}\}
• C= \{ \text{letters of the word `llama'}\}

Explain the meaning of "the complement of set A."

A set is defined as A=\left\{ x:0\leq x \leq 5 \text{ and }x \text{ is an integer} \right\}.

Consider the sets A=\left\{ x:-6\lt x \lt 6 \text{ and }x \text{ is an integer} \right\} and \\ B=\left\{ x:-1\leq x \leq 10 \text{ and }x \text{ is an integer} \right\}.

State whether the following points are in the set A=\left\{(x, y) : y = 5x-7 \right\}:

Consider the sets A=\left\{(x, y) : y = 3x-4 \right\} and B=\left\{(x, y) : y = 2x+6 \right\}.

Explain the meaning of the following statements:

P and Q are sets of vegetable types:

P= \{carrots, cauliflowers, beans\}; Q = \{cauliflowers, potatoes\}

There are no other vegetable types in universal set U.

Suppose set A = \left\{3, 4, 5, 6, 7\right\} and set B = \left\{3, 7, 8, 9\right\}. Find A \cap B.

List the elements of A \cap B given the following sets:

If A is the set of factors of 24, and B is the set of factors of 36, then list the elements of:

Set A is the set of possible outcomes from rolling a standard die, and set B is the set of possible outcomes from rolling an eight-sided die. List the elements of the following sets:

P and Q are sets of flower varieties:

P= \{roses, lillies, daisies\}; Q= \{lillies, sunflowers\}

There are no other flower varieties in universal set U.

The sets V = \left\{21, 8, 30, 9, 28\right\} and W = \left\{21, 8, 30, 9, 28, 7, 13, 12, 26\right\} are such that there are no other elements outside of these two sets.

Consider the following sets:

A = \left\{1, 2, 3, 4, 5, 6, 7\right\},B = \left\{1, 2, 3, 4\right\}

If there are no elements contained outside of these sets, find:

Consider the following sets:

\\

Consider the sets A=\left\{ x:-7\leq x \leq 10 \text{ and }x \text{ is an integer} \right\}, B=\left\{-2, 4, 8\right\} and \\ C=\left\{3, -5, 11\right\}.

For each of the following, identify the Venn diagram that best represents the sets A and B:

Venn diagram 1

Venn diagram 3

Venn diagram 2

Venn diagram 4

We are interested in the colour of a card randomly drawn from a standard deck. Draw a Venn diagram to illustrates this.

The Venn diagram shows the number of students in a school playing Rugby League (L), Rugby Union (U), both or neither.

a

Complete the table of values below:

	Play Rugby League	Don't play Rugby League
Play Rugby Union
Don't play Rugby Union

b

Find the following:

i

n(L\cap{U}')

ii

n(L)

iii

n(U)

iv

n(U\cap L')

v

n({L}')

vi

n({U}')