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

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that each word contain 2vowles and 3consonant

Rational and irrational numbers, RATIONAL NUMBERS All numbers of the ty...

RATIONAL NUMBERS All numbers of the type p/q where p and q are integer and q ≠0, are known as rational. Thus  it can be noticed that every integer is a rational number

Mathematical model representing the total parking cost, John has a choice o...

John has a choice of using one of two parking garages when he visits downtown: Option1:  $8 an hour for the first two hours, then $2 and hour for each hour more than 2; or Op

Geometry, what shapes can go into a triangular prism

what shapes can go into a triangular prism

Equation, Solve : 4x2+2x+3=0 Ans) x^2 + (1/2)x = -(3/4) (x+1/4)^2 = 1/...

Solve : 4x2+2x+3=0 Ans) x^2 + (1/2)x = -(3/4) (x+1/4)^2 = 1/16 - 3/4 = -11/16 implies x = (-1+i(11)^(1/2))/4 and its conjugate.

Triangles, ABCD is a parallelogram which AB and CD are divides by P and Q. ...

ABCD is a parallelogram which AB and CD are divides by P and Q. Such that AP:PB=3:2 and CQ:QD=4:1. If PQ and AC are meet at R, show that AR=3/7AC.

Characteristics and limitations of moving average, Characteristics and Limi...

Characteristics and Limitations of moving average Characteristics of moving average 1) The more the number of periods in the moving average, the greater the smoothing

Linear equation, develop any two linear equation which are reducible into l...

develop any two linear equation which are reducible into linear form from our daily life by cross multiplication

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