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

Basic, 8l550ml - 1/4l =

8l550ml - 1/4l =

Minimizes the sum of the two distance, The value of y that minimizes the su...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

Probability, an insurance salesman sells policies to 5 men, all of identica...

an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p

Interpretations of definite integral, Interpretations of Definite Integral ...

Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini

Fractions, what is the lowest term of 11/121

what is the lowest term of 11/121

Process for solving linear equations, 1. If the equation has any fractions ...

1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al

Introduction To Numerical Methods & Matlab, Can you help me with the course...

Can you help me with the coursework i have in Matlab?

Determine the differential y = t 3 - 4t 2 + 7t, Determine the differentia...

Determine the differential for following.                                      y = t 3 - 4t 2 + 7t Solution Before working any of these we have to first discuss just

Área de un rectangulo, calcula el área de la región sombreada de un rectáng...

calcula el área de la región sombreada de un rectángulo cuya base es 12.6 cm y su altura es 8.4

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