62 476
Assignments Done
98,8%
Successfully Done
In June 2018

Answer to Question #15483 in Analytic Geometry for Sujata Roy

Question #15483
If lattice (C,<=) is a complemented chain, then
a) |C|<=1
b) |C|<=2
c) |C|>1
d) doesn't exist.
Expert's answer
Every chain is bounded: 0 and 1 belongs to C, or they coicide, so |C|=1.
If there is third element a, then its complement is such b, that inf(a,b)=0 and
sup(a,b)=1. But as it is chain, then we have a<=b or b<=a. If a<=b then
0=inf(a,b)=a and 1=sup(a,b)=b. Case b<=a is similar.

So there cannot be other third element in C.

|C|=2 or |C|=1 => |C|<=2

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions