What is partially ordered set, Mathematics

Assignment Help:

What is Partially Ordered Set?  Let  S = {a,b,c} and A = P(S). Draw the Hasse diagram of the poset A with the partial order ⊆ (set inclusion).  

Ans: Let R be a relation defined on a non-empty set A. The mathematical structure (A, R) is set to be a Partial order set or poset if the relation R is a partial order relation on A. 

Any relation R defined on a non-empty set A is said to be a Partial Order Relation, if R is 

  • Reflexive on A i.e., xRx ∀ x∈ A
  • Anti-symmetric on A i.e., xRy and yRx ⇒ x = y and
  • Transitive on A i.e., xRy and yRz ⇒ xRz for x, y, z ∈ A.

A partial order relation is denoted by the symbol '≤'.  A general notation for a poset is (A, ≤), where A is any non-empty set and '≤' is any partial order relation defined on the set A.  The Hasse diagram for the poset (P(S),  ⊆) is as below. The poset has 8 elements - 8 possible subsets of S. Null set is the minimum element and S itself is the maximal element.

 

140_What is Partially Ordered Set.png

 


Related Discussions:- What is partially ordered set

Geometry, #question.onstruct/draw geometric shapes with specific condition....

#question.onstruct/draw geometric shapes with specific condition.

Trapezoid rule - approximating definite integrals, Trapezoid Rule - Approxi...

Trapezoid Rule - Approximating Definite Integrals For this rule we will do similar set up as for the Midpoint Rule. We will break up the interval [a, b] into n subintervals of

Word problem solving, the traffic light at three different road crossing ch...

the traffic light at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. if they change simultaneously at 7 a.m., at what time wil

Evaluate the infinite limits of given limits, Evaluate following limits. ...

Evaluate following limits. Solution Therefore we will taking a look at a couple of one-sided limits in addition to the normal limit here. In all three cases notice

Determine matrix of transformation for orthogonal projection, Determine the...

Determine the matrix of transformation for the orthogonal projection onto the line L that passes through the origin and is in the direction Û=(3/13 , 4/13 , 12/13). Determine the r

Hydrostatic pressure and force - applications of integrals, Hydrostatic Pre...

Hydrostatic Pressure and Force - Applications of integrals In this part we are going to submerge a vertical plate in water and we wish to know the force that is exerted on t

Marketing of herbal products , To help Himalya herbal launch a successful m...

To help Himalya herbal launch a successful marketing campaign in the UK

Payoff Matrix, A farmer grows apples on her 400-acre farm and must cope wit...

A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"

Wavy curve method, In order to compute the inequalities of the form ...

In order to compute the inequalities of the form   where n 1 , n 2 , ....... , n k , m 1 , m 2 , ....... , m p are natural and real numbers and a 1 , a 2 , ... , a k ,

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