1-3 Sets and Domains

Goals:1. Use the operations of union and

intersection to find solution sets.

2. Represent solution sets of unions and intersections on number lines and in Venn diagrams.

Intersection of Sets

You are reading a police report. It says an accident took place in the intersection of Main Street and Lincoln Avenue.

What does that mean?

Intersection of Sets

In Algebra, the term intersection has a similar meaning when used with sets.

The intersection of sets A and B, written A ∩ B, is the set of elements that are in both A and B.

Intersection of Sets

Example:

Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }.

Give the intersection of A and B.

Intersection of Sets: Venn Diagrams

Example:

Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }.

Give the intersection of A and B.

1 3 6

2 5

8 13

4 7

11

A ∩ B is the region in the middle where the circles intersect. Shade this area.

Union of Sets

The union of sets A and B, written A U B, is the set of elements that are in either A or B (or both).

Write each number only once.

Union of Sets

Example:

Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }.

Give the union of A and B.

Union of Sets: Venn Diagrams

Example:

Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }.

Give the union of A and B.

1 3 6

2 5

8 13

4 7

11

A U B is the entire region Shade this area.

Empty Set or Null Set

Empty set or null set is a set that contains no members.

Represented as { } or ø

Can you think of an example?

Empty Set or Null SetEmpty set or null set is a set that contains no members.

Example:

Let S = the set of even integers, and T = the set of odd integers.

Find S ∩ T.

No integer is both odd and even, so:

S ∩ T = { }

Activity

Find a partner.1. Write down your full name.2. Make one set for each person. 3. Label each set using a letter to represent that

person.4. Include all the letters in your name in your set

(Remember: each letter should only appear once).5. Find both the intersection and union for the two

sets. 6. Write the intersection and union using braces and

using a Venn Diagram.

Graphs of Intersections and Unions

Graph the set of all numbers s such that s > -2 or s < -10.

The word or means that you need to find the union.

ExampleThe label on a paint can says, “For best results, do not use if

the temperature is above 90° or below 50°.”

a. Use an inequality to describe each interval in which you should not paint.

b. Graph the temperature in which you should not paint. Then graph the recommended temperatures for painting, and describe them with an inequality.

a. What temperatures are recommended for painting?

Follow Up

Work with a partner or by yourself to complete 1-15 odd on pages 21-22.

Begin homework.