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
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
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.2: Indirect Proof
Problem 12E: Which of the following statements would you prove by the indirect method? a If ACAB in ABC, then...
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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
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