In Class Activity
MAT 300, Spring 2004
February 10, 2004
Consider Interval Sets
Define the sets A,B, and C as follows: ]}8,3(|{
∈
ℜ
∈
=
xxA , }52|{ ≤<−ℜ
∈
=
xxB ,
and .
}0|{ ≤ℜ∈= xxC
Using set builder notation describe the following sets:
•
B
A
∪
•
CA∩
•
CBA ∪∩ )(
Differences
Here are some informal notes from our book about two other useful sets:
• The difference X\Y is the set of all elements in X that are not in Y.
• The symmetric difference X∆Y is the set of elements that are either in X or Y, but not
both.
1. Using set builder notation and the sets defined above, define the following sets:
• B\A
• A∆B
2. Find two ways of writing each of these sets in terms of compliments, intersections
and unions.
Proof
Prove the following statement.
A
∩
B =
∅
if and only if A\B = A
