AFAM INTERVAL NOTATION Notes: Mrs. Buchen

AFAM

Notes: INTERVAL NOTATION

Remember: Inequality form of graphing on a number line.

A) x 2

Mrs. Buchen

***Rewrite inequality form to interval notation using and

B) y > -3

C) h < 0

D) m 4 SET BUILDER NOTATION Open Interval: {x l a < x < b} (DOES NOT INCLUDE ENDPOINTS) Instead of using open circles, use parenthesis.

Closed Interval: {x l a x b}

(INCLUDES ENDPOINTS)

Instead of using closed circles, use brackets.

Half -Open Interval:

{x l a < x b} (Not Include a, includes b)

x l a x < b} (Includes a, not include b)

EXAMPLES: Write the interval in set builder notation.

1) (-2, 4)

2) [ 1, 5 ]

3) [ 3, )

4) (- , 5]

EXAMPLES: Write the set builder notation into interval notation.

1) { x l x > 1 } 3) { x l x 5 }

2) { x l -3 < x 1 } 4) { x l 0 x < 1 }

EXAMPLES: Graph the following using interval notation on a number line.

1) ( - , 4]

2) ( -3, ) 3) { x l -2 x < 3 } 4) { x l -5 < x 0 } 5) { x l x 1}

6) { x l x > -2 } 7) (-2, 5]

UNION AND INTERSECTION OF SETS

Just like you can perform operation on real numbers (+, -, , , ) , you can perform

operations on sets.

The union of two sets, written as A B, is the set of all elements that belong to

either A or B. Set Builder Notation:

A B = { x l x A or x B }

= Set membership = Denial of set membership

For example: If A = { 2, 3, 4} and B = { 0 ,1 ,2, 3, 4} then A B = { 0, 1, 2, 3, 4}.

Notice that elements in both sets are only listed once.

The intersection of two sets, written as A B, is the set of all elements that are common

to both A and B.

Set Builder Notation:

A B = { x l x A and x B } For example: If A = { 2, 3, 4} and B = {0 ,1 ,2, 3} then A B = { 2, 3, }.

Also, if A = { 2, 3, 4} and B = {7, 8}. Then the intersection would be an empty set.

We call the sets __________________. So A B = (Null set)

Examples: Find the intersection or union given

A = {0, 2, 4, 6, 10, 12} B = { 0, 3, 6, 12, 15} and C = {1, 2, 3, 4, 5, 6, 7}

1. A C

2. B C

3. A ( B C)

4. B ( A C)

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download