Solution Found!
Prove the complement laws in Table 1 by showing thata)
Chapter 1, Problem 9E(choose chapter or problem)
In Exercises 5–10 assume that \(A\) is a subset of some underlying universal set \(U\).
Prove the complement laws in Table 1 by showing that
a) \(A \cup \bar{A}=U\).
b) \(A \cap \bar{A}=\emptyset\).
Equation Transcription:
∅
Text Transcription:
A
U
A cup A=U
A cap A=emptyset
Questions & Answers
QUESTION:
In Exercises 5–10 assume that \(A\) is a subset of some underlying universal set \(U\).
Prove the complement laws in Table 1 by showing that
a) \(A \cup \bar{A}=U\).
b) \(A \cap \bar{A}=\emptyset\).
Equation Transcription:
∅
Text Transcription:
A
U
A cup A=U
A cap A=emptyset
ANSWER:
Solution:
Step1
Given that
The complement laws .
Step2
To find
We have to prove the complement laws.
Step3
Complement laws :- The supplement of a set B refers to components not in B.
a)
Here , Right hand side=
And Left hand side=