Let A and B be distinct elements in T. Show that An BET. Case 1: A and B = R AnB =Øn R=Ø E T by a. Case 2: A = Ø and B = (-∞,a) Case 3: A =R and B = = (-∞,a) Case 4: A = (-∞,a) and B = (-∞,b) where a,b € R. WLOG, a > b.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 5TFE
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Let A and B be distinct elements in T. Show that A n BET.
Case 1: A
and B = R
AnB =Øn R = Ø E T by a.
Case 2: A = Ø and B = (-∞,a)
Case 3: A =R and B = (-∞,a)
Case 4: A = (-∞,a) and B = (-∞,b) where a,b € R.
WLOG, a > b.
Transcribed Image Text:Let A and B be distinct elements in T. Show that A n BET. Case 1: A and B = R AnB =Øn R = Ø E T by a. Case 2: A = Ø and B = (-∞,a) Case 3: A =R and B = (-∞,a) Case 4: A = (-∞,a) and B = (-∞,b) where a,b € R. WLOG, a > b.
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