Let U be a universal set and A, B,C C U. ITEM 1. Prove: AOB C AU B (A U B)C = A° n BC Here, AC and BC denote set complement. Use De Morgan's Law for negation of OR to prove this. ITEM 2. Prove: ITEM 3. Prove: If A C B and B C C, then A C C.
Let U be a universal set and A, B,C C U. ITEM 1. Prove: AOB C AU B (A U B)C = A° n BC Here, AC and BC denote set complement. Use De Morgan's Law for negation of OR to prove this. ITEM 2. Prove: ITEM 3. Prove: If A C B and B C C, then A C C.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 12E: For the sets given in Exercise 9, is there a distributive relationship for intersection with respect...
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Prove the following set-theoretic properties using definitions of the given set relations and set operations. Your proofs should properly identify the logical equivalences and valid argument forms that justifies the result.
Transcribed Image Text:Let U be a universal set and A, B,C C U.
ITEM 1. Prove:
AOB C AU B
(A U B)C = AC n BC
Here, AC and BC denote set complement.
Use De Morgan's Law for negation of OR to prove this.
ITEM 2. Prove:
ITEM 3. Prove:
If A C B and B C C, then A C C.
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