Prove that the poset has a unique least element, Mathematics

Assignment Help:

Prove that the Poset has a unique least element

Prove that if (A, <) has a least element, then (A,≤)  has a unique least element.

Ans: Let (A, ≤) be a poset. Suppose the poset A has two least elements x and y. Since x is the least element, it implies that x ≤ y. Using the same argument, we can say that y ≤ x, since y is supposed to be another least element of the same poset. ≤ is an anti-symmetric relation, so x ≤ y and y ≤ x ⇒ x = y. Thus, there is at most one least element in any poset.


Related Discussions:- Prove that the poset has a unique least element

How to make equations of conics easier to read, How to Make Equations of Co...

How to Make Equations of Conics Easier to Read ? If you want to graph a conic sections, first you need to make the equation easy to read. For example, say you have the equatio

Setofoperations, write CxD being sure to use appropriate brackets and find ...

write CxD being sure to use appropriate brackets and find n(CxD)

Repeated roots, Under this section we will be looking at the previous case ...

Under this section we will be looking at the previous case for the constant coefficient and linear and homogeneous second order differential equations.  In this case we need soluti

Find a longest common substring - suffix trees, 1. Using suffix trees, give...

1. Using suffix trees, give an algorithm to find a longest common substring shared among three input strings: s 1 of length n 1 , s 2 of length n 2 and s 3 of length n 3 .

Two bulbs are selected without replacement, A bag of 28 tulip bulbs contain...

A bag of 28 tulip bulbs contains 12 red tulip bulbs,7 purple tulip bulbs  and 9 yellow tulip bulbs,. Two bulbs are selected without replacement. Determine, a)    The probability t

Change of base of logarithms, Change of base: The final topic that we have...

Change of base: The final topic that we have to look at in this section is the change of base formula for logarithms. The change of base formula is,

Retail price index, Retail price index This is weighted average of pri...

Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd