Set Theory

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# Set Theory - PowerPoint PPT Presentation

Set Theory. A2 Set Functions. Set Functions. Everything together. What they have the SAME. What is NOT in the set (cross out). Examples. 1. Given P = {1, 3, 5, 7, 9} and Q = {0, 2, 4, 6, 8}, find Intersection of P and Q ___________________ Union of P and Q ________________________.

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### Set Theory

A2 Set Functions

Set Functions

Everything together

What they have the SAME

What is NOT in the set (cross out)

Examples

1. Given P = {1, 3, 5, 7, 9} and Q = {0, 2, 4, 6, 8}, find

Intersection of P and Q ___________________

Union of P and Q ________________________

{ }

Do NOT write 0!

{ 0,

1,

2,

3,

4,

5,

6,

7,

8,

9

}

What they have the SAME

Everything together

No

They have nothing the same

Need to write it in ORDER

This is called the Empty set

Examples

2. Given A = {0, 2, 4, 6, 8, 10} B = {0, 2, 3, 5, 6} C = {0, 1, 2, 3, 4, 5}

• What is A∩B? _________________________

b. What is A∩B∩C? ________________________

c. What is BUC? ___________________________

d. What is AUB? ___________________________

{

0

, 2

, 6

}

{

0

, 2

}

{

0

, 1

, 2

, 3

, 4

, 5

, 6

}

{

0

, 2

, 3

, 4

, 5

, 6

, 8

, 10

}

Examples

X

X

X

X

3. Given: Set U = {1, 2, 3, 4, 5, 6, 7, 8}

Set B = {2, 3, 5, 6}

Set B is a subset of set U, what is the compliment of set B?

a. { } c. {2, 3, 5, 6}

b. {1, 4, 7, 8} d. {1, 2, 3, 4, 5, 6, 7, 8}

What is NOT in the set

Cross out everything that is in the SUBSET

What is left?

4. Given:

A = {all even integers from 2 through 20, inclusive}

B = {2, 6, 10, 14, 16}

What is the complement of set B within set A?

a. {2, 6, 10, 14, 16}

• {4, 8, 12, 18}
• {4, 8, 12, 18, 20}

d. {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

2

X

4

6

X

8

10

X

12

14

X

16

X

18

20

Examples

5. Given

Find the intersection of A and B ___________

Find A U C ____________________________

Find the intersection of A, B, and C __________

{ 1, 2, 3}

{ 1, 2, 3, 4, 5, 6, 7, 9}

{ 1, 3}

What they have the SAME

Union

What they have the SAME

Everything together

Everything that is blue

Examples

6. Maureen tracks the range of outdoor temperatures over three days. She records the following information. Express the intersection of the three sets as an inequality in terms of temperature t _______________

0

≤ ≤

t

40

What they have the SAME

Do they all have 0?

Do they all have 40?

Do they all have 45?

Do they all have 50?

Do they all have -20?

Do they all have -23?

No

Yes

Yes

No

No

No

Practice Problems

Now try the practice problems on your own