SECTION 2.6 Set Operations and Compound Inequalities 103
Finding the Intersection of Two SetsLet and Find
The set contains those elements that belong to both A and B: the numbers
2 and 4. Therefore,
NOW TRYA compound inequalityconsists of two inequalities linked by a connective word.
and
2 x 74 or 3 x- 665
x+ 1 ... 9 x- 2 Ú 3
= 52 , 46.
A ̈B= 5 1, 2 , 3, 46 ̈ 52 , 4 , 6 6
A ̈B
A= 5 1, 2, 3, 4 6 B= 5 2, 4, 6 6. A ̈B.
EXAMPLE 1
OBJECTIVE 2 Solve compound inequalities with the word and.We use the
following steps to solve a compound inequality such as “x+ 1 ... 9 and x- 2 Ú3.”
Examples of compound inequalities
linked by andor orOBJECTIVES
Set Operations and Compound Inequalities
2.6
1 Find the
intersection
of two sets.
2 Solve compound
inequalities with
the word and.
3 Find the union of
two sets.
4 Solve compound
inequalities with
the word or.Consider the two sets Aand Bdefined as follows.
The set of all elements that belong to both AandB, called their intersectionand sym-
bolized , is given by
IntersectionThe set of all elements that belong to either AorB, or both, called their unionand
symbolized , is given by
UnionWe discuss the use of the words andand oras they relate to sets and inequalities.
OBJECTIVE 1 Find the intersection of two sets.The intersection of two sets
is defined with the word and.
A ́B= 5 1, 2, 3, 4 6.
AªB
A ̈B= 5 2, 3 6.
AºB
A= 5 1, 2, 3 6 , B= 5 2, 3, 4 6
NOW TRY
EXERCISE 1
Let and
. Find
A ̈B.
B= 5 0, 2, 6, 8 6
A= 5 2, 4, 6, 8 6
Intersection of SetsFor any two sets Aand B, the intersectionof Aand B, symbolized is
defined as follows.
A ̈B= 5 x |x is an element of A and x is an element of B 6
A ̈B,
ABNOW TRY ANSWER
- 5 2, 6, 8 6
Solving a Compound Inequality with and
Step 1 Solve each inequality individually.
Step 2 Since the inequalities are joined with and,the solution set of the
compound inequality will include all numbers that satisfy both in-
equalities in Step 1 (the intersection of the solution sets).