4.2 1

Section 4.2Intersections, Unions & Compound Inequalities

Using Set Diagrams and Notation Intersections of Sets

Conjunctions of Sentences and Unions of Sets

Disjunctions of Sentences or More Interval Notation Specifying Domains

BA

}5,4{{1,2,3}

[11,17),4)(- )[-2,

4.2 2

Sets and Compound Inequalities

Compound Inequalities: Two inequalities joined by and or or

Intersection Union Members in Common All Members in Both

“and” “or”

4.2 3

Intersection: Members in Common

(

)

)(

4.2 4

Notation:Abbreviated Compound Inequalities

4.2 5

Solve & Graph

buildersetxx

notationerval

ebraicax

nowx

x

43|

int)4,3[

lg43

)2(826

555

13521

[ )

4.2 6

(both must be true)Solve & Graph a Conjunction and

}3|{}3|{}1|{),3(

3

31

15522

2255

1725352

515

55

22

22

xxxxxx

x

xandx

and

xandx

and

xandx

xx

[

(

(

4.2 7

No Solutions:Disjoint Sets The Empty Set

4.2 8

(both must be true)Solve & Graph a Disjoint Conjunction

}1|{}2|{

12

3342

1133

213132

33

33

24

22

xxxx

xandx

and

xandx

and

xandx

xx

(

)

4.2 9

Union: All Members in Both Sets

(

)

) (

4.2 10

(either can be true)Solve & Graph a Union or

),2[)4,(

}2|{}4|{

24

10582

131377

3513127

510

55

28

22

xxxx

xorx

or

xorx

or

xorx

xx

[

)

) [

4.2 11

),()7,(

}7|{

7

"

732

3355

103252

23

23

23

23

22

xorxx

xorx

or

xorx

or

xorx

x

Try another … (either can be true)Solve & Graph a Union or

()

(

)

4.2 12

The Biggest Possible Solution

[

)

4.2 13

Expressing DomainsWith Interval Notation

),2[

2

02

?2)(

x

x

xxfaboutWhat

[

()

4.2 14

Where do we go from here? … Section

4.3 Absolute Value Equations & Inequalities