Beginning Algebra, 11th Edition

Finding the Intersection of Two Sets

Suppose that and Find

each of the following.

(a) (b) (c)

NOW TRY

Sets like Pand Rin Example 6that have no elements in common are called

disjoint sets.The Venn diagram in FIGURE 5shows a pair of disjoint sets.

P ̈Q= 5 3, 27 6 Q ̈R= 5 2, 10, 28 6 =R P ̈R= 0

P= 5 3, 9, 27 6 ,Q= 5 2, 3, 10, 18, 27, 28 6 , R= 5 2, 10, 28 6.

EXAMPLE 6

600 APPENDIX A Sets

U

A B

A ∩ B is shaded.

U

Disjoint sets; A ∩ B = Ø

A B

FIGURE 4

FIGURE 5

Using Set Operations

Let and

Find each of the following.

(a) (b)

(c) (d)

(e) A¿= 5 5, 7 6 = B NOW TRY

B ́C = 5 2, 5, 7 6 =C B ̈C = 5 5, 7 6 =B

A ́B= 5 2, 5, 7, 10, 14, 20 6 =U A ̈B= 0

U= 5 2, 5, 7, 10, 14, 20 6 ,A= 5 2, 10, 14, 20 6 ,B= 5 5, 7 6 , C= 5 2, 5, 7 6.

EXAMPLE 7

NOW TRY
EXERCISE 6
If and
N= 5 0, 3, 6, 9 6 ,find M ̈N.

M= 5 1, 3, 5, 7, 9 6

NOW TRY ANSWERS

6. 5 3, 9 6

NOW TRY
EXERCISE 7
Let

and

Find each of the following.

(a)B ́C (b)A ̈B (c) C¿

C= 556.

B= 5 2, 5, 8 6 ,

A= 5 1, 4, 7, 9, 10 6 ,

U= 5 1, 2, 4, 5, 7, 8, 9, 10 6 ,

7. (a) (b)
   (c) 5 1, 2, 4, 7, 8, 9, 10 6

5 2, 5, 8 6 =B 0

EXERCISES

List the elements of each set. See Examples 1 and 2.

1.The set of all natural numbers less than 8

2.The set of all integers between 4 and 10

3.The set of seasons

4.The set of months of the year

5.The set of women presidents of the United States before 2008

6.The set of all living humans who are more than 200 years old

7.The set of letters of the alphabet between K and M

8.The set of letters of the alphabet between D and H

The shaded region in FIGURE 4represents the intersection of the two sets Aand B.

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