Solution Found!
Show that if A and B are sets, then
Chapter 1, Problem 19E(choose chapter or problem)
Show that if \(A\) and \(B\) are sets, then
a) \(A-B=A \cap \bar{B}\)
.
b) \((A \cap B) \cup(A \cap \bar{B})=A\).
Equation Transcription:
Text Transcription:
A
B
A − B = A cap bar bar B
(A cap B) cup (A cap bar B) = A
Questions & Answers
QUESTION:
Show that if \(A\) and \(B\) are sets, then
a) \(A-B=A \cap \bar{B}\)
.
b) \((A \cap B) \cup(A \cap \bar{B})=A\).
Equation Transcription:
Text Transcription:
A
B
A − B = A cap bar bar B
(A cap B) cup (A cap bar B) = A
ANSWER:
Solution :
Step 1:
In this problem we have to show these conditions , where A and B are two sets.
Formulas: 1. = X - B,
2. A A = A
3. AA =
Definitions:
Union: the union of the sets A and B , denoted by , which is the set that contains those element that are either in A or in B , or in both.
Therefore = {
}.
Intersection : the intersection of the sets A and B , it is denoted by , which is the set containing those elements in both A and B.
Therefore .
Set difference : the difference of A and B is denoted by A -B, which is the set containing the element of A that are not in B .
A - B = { }=