Set Theory

Set Theory

By the end of the lesson, I will be able to...

• Draw Venn Diagrams based on events.

• Distinguish between universal sets and subsets.

• Find intersections, unions, and complements between multiple sets.

Review of Venn Diagrams

​I can draw Venn Diagrams based on events.

Draw

A group of 50 people were asked whether they like pizza and burgers. 10 people answered that they don't like pizza or burgers at all. 20 people liked both pizza and burgers and 12 people only liked pizza. Complete the Venn Diagram.

Review of Venn Diagrams

​I can draw Venn Diagrams based on events.

​A group of 50 people were asked whether they like pizza and burgers. 10 people answered that they don't like pizza or burgers at all. 20 people liked both pizza and burgers and 12 people only liked pizza.

Draw

We asked 30 students whether they like Math or Science. 10 students like both math and science, 4 students said they only like Science. 6 students answered that they like Math but not Science. Complete the Venn Diagram.

Review of Venn Diagrams

​I can draw Venn Diagrams based on events.

We asked 30 students whether they like Math or Science. 10 students like both math and science, 4 students said they only like Science. 6 students answered that they like Math but not Science.

Draw

A group of 50 people were asked whether they like pizza and burgers. 10 people answered that they don't like pizza nor burgers at all. 20 people like both pizza and burgers and 12 people only liked pizza. Complete the Venn Diagram.

Set Theory

​I can distinguish between universal sets and subsets.

Open Ended

Come up with your own example of a universal set. (It can be anything with multiple elements). Name the set and then list the elements in the set.

EXAMPLE:

Single Digit Whole Numbers

$$U=\left\{0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9\right\}$$

Open Ended

Now, define a subset from your universal set. This can have multiple elements or just a single element.

EXAMPLE:

Single-Digit Whole Numbers

$$U=\left\{0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9\right\}$$

Subset: Odd Single-Digit Whole Numbers

$$A=\left\{1,\ 3,\ 5,\ 7,\ 9\right\}$$

Set Theory

​I can find intersections, unions, and complements between multiple sets.

Multiple Choice

Set A: Students at Mount Vernon that will be graduating this year.

Set B: Male students at Mount Vernon.

What is $$A\cap B$$ ?

• Male students that will not be graduating this year at Mount Vernon.

• Female students that will be graduating this year at Mount Vernon.

• Male students that will be graduating this year at Mount Vernon.

• Female students that will not be graduating this year at Mount Vernon.

Multiple Choice

$$Set\ A:\ \left\{1,\ 8,\ 9,\ 12\right\}$$

$$Set\ B:\ \left\{1,\ 3,\ 5,\ 6,\ 7\right\}$$

What is $$A\cap B$$ ?

• $$\left\{1,\ 8,\ 9,\ 12\right\}$$

• $$\left\{3,\ 5,\ 6,\ 7\right\}$$

• $$\left\{1,\ 3,\ 5,\ 6,\ 7,\ 8,\ 9,\ 12\right\}$$

• $$\left\{1\right\}$$

Set Theory

​I can find intersections, unions, and complements between multiple sets.

Multiple Choice

Set A: Students at Mount Vernon that will be graduating this year.

Set B: Male students at Mount Vernon.

What is $$A\cup B$$ ?

• All of the students that will either be graduating this year or are female at Mount Vernon.

• All of the students that will either be graduating this year or are male at Mount Vernon.

• All of the students that are male and will be graduating this year at Mount Vernon.

• All of the students that are female and will be graduating this year at Mount Vernon.

Multiple Choice

$$Set\ A:\ \left\{2,\ 3,\ 7,\ 9\right\}$$

$$Set\ B:\ \left\{2,\ 3,\ 5,\ 6,\ 8\right\}$$

What is $$A\cup B$$ ?

• $$\left\{5,\ 6,\ 7,\ 8,\ 9\right\}$$

• $$\left\{2,\ 3,\ 5,\ 6,\ 7,\ 8,\ 9\right\}$$

• $$\left\{5,\ 6,\ 8\right\}$$

• $$\left\{2,\ 2,\ 3,\ 3,\ 5,\ 6,\ 7,\ 8,\ 9\right\}$$

Set Theory

​I can find intersections, unions, and complements between multiple sets.

Multiple Choice

Set A: Students at Mount Vernon that will be graduating this year.

Set B: Male students at Mount Vernon.

What is $$A'$$ ?

• All of the female students that will be graduating at Mount Vernon this year.

• All of the male students that will not be graduating at Mount Vernon this year.

• All of the students at Mount Vernon that will not be graduating this year.

• All of the female students that will not be graduating at Mount Vernon this year.

Multiple Choice

Set A: Students at Mount Vernon that will be graduating this year.

Set B: Male students at Mount Vernon.

What is $$\overline{B}$$ ?

• All of the female students that will be graduating at Mount Vernon this year.

• All of the male students that will not be graduating at Mount Vernon this year.

• All of the students at Mount Vernon that will not be graduating this year.

• All of the female students that will not be graduating at Mount Vernon this year.

Multiple Choice

$$Universal\ Set:\ \left\{3,\ 4,\ 5,\ 6,\ 8,\ 9\right\}$$

$$Subset\ B:\ \left\{3,\ 4,\ 6,\ 9\right\}$$

What is the complement of $$Set\ B$$ ?

• $$\left\{3,\ 4,\ 5,\ 6,\ 9\right\}$$

• $$\left\{3,\ 4,\ 6,\ 9\right\}$$

• $$\left\{3,\ 4,\ 5,\ 6,\ 8,\ 9\right\}$$

• $$\left\{5,\ 8\right\}$$

Set Theory

​I can find intersections, unions, and complements between multiple sets.

​Complete the two examples on the back of your handout.

​I can find intersections, unions, and complements between multiple sets.

​I can find intersections, unions, and complements between multiple sets.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Define the Universal Set.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Define the two subsets.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Draw a Venn diagram to represent the sets.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Find the intersection of F and B.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Find the union of F and B.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Find F'.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Find B'.

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Find $$\overline{F\cap B}$$ .

Draw

Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, Kara, and Todd said football. Joseph, Lydia, and Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. Find $$\overline{F\cup B}$$ .

Fill in the Blank

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

How many students does Mr. Cagle have?

Fill in the Blank

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

How many students have cats?

Fill in the Blank

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

How many students are in the region $$C\cap D$$ ?

Open Ended

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

What does the region $$C\cap D$$ represent in words?

Fill in the Blank

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

How many students are in the region $$C'$$ ?

Open Ended

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

What does the region $$C'$$ represent in words?

Fill in the Blank

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

How many students are in the region $$C\cup D$$ ?

Open Ended

Mr. Cagle surveys his class about the pets they have at home. He creates a Venn diagram to represent his findings.

$$C\ =\ \left\{has\ cats\right\}$$

$$D\ =\ \left\{has\ dogs\right\}$$

What does the region $$C\cup D$$ represent in words?

Draw

Create a Venn diagram with the following sets: (The Universal set will include only letters from these 3 sets) A= {the letters in America}, C={the letters in Cambodia}, D={the letters in Denmark}

Open Ended

List the elements of $$A\cup D$$ .

Open Ended

List the elements of $$C\cap D$$ .

Fill in the Blank

How many elements are in $$D'$$ ?

Open Ended

List the elements of $$\overline{A\cup D}$$ .

Open Ended

List the elements of $$\overline{A\cap C}$$ .

Open Ended

List the elements of $$A\cap C\cap D$$ .