Consider the following statement. For all sets A and B, ((A° U B°) -A) = A. An alternative proof is shown in Appendix B. Proof: Suppose A and B are any sets. Then, ((AC U Bº) - A) C = ((Ac U Bc) n Ac)c = (Acn (Aº U Bc)) = = = || || by the set difference law by the commutative law for n ((Aºn Aº) U (Aºn B)) by the distributive law (AC U (Aºn B°)) ---Select--- (AC)C ---Select--- ---Select--- = A X X

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Selections are: by the absorption law, by the associative law, by the commutative law, by de Morgan's law, by the distributive law, by the double complement law, by the idempotent law, by the identity law, and by the universal bound law

Consider the following statement.
For all sets A and B, ((A° U B°) -A) = A.
An alternative proof is shown in Appendix B.
Proof: Suppose A and B are any sets. Then,
((AC U Bº) - A) C =
=
=
=
=
|| ||
((AC U Bc) n Ac)c
(Acn (Aº U Bc))
((Aºn Aº) U (Aºn B)) by the distributive law
(AC U (Aºn B°))
---Select---
(AC)C
---Select---
---Select---
by the set difference law
by the commutative law for n
= A
X
X
Transcribed Image Text:Consider the following statement. For all sets A and B, ((A° U B°) -A) = A. An alternative proof is shown in Appendix B. Proof: Suppose A and B are any sets. Then, ((AC U Bº) - A) C = = = = = || || ((AC U Bc) n Ac)c (Acn (Aº U Bc)) ((Aºn Aº) U (Aºn B)) by the distributive law (AC U (Aºn B°)) ---Select--- (AC)C ---Select--- ---Select--- by the set difference law by the commutative law for n = A X X
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