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

Divides a given line-segment externally in the ratio of 1:2, Divides a give...

Divides a given line-segment externally in the ratio of 1:2 Construction: i )Draw BX making an actueangle at B. ii) Starting from B, mark 2 equal points on BX as shown in the f

Determine the team having similar code-pigeon hole principle, Shirts number...

Shirts numbered consecutively from 1 to 20 are worn by 20 members of a bowling league. While any three of these members are selected to be a team, the league aims to use the sum of

Advanced functions, writ the equation that describes the motion of a point ...

writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a

Statistics, How do you calculate for the distance between two co-ordinates?...

How do you calculate for the distance between two co-ordinates?

Finds out the center and radius of circle, Finds out the center & radius of...

Finds out the center & radius of each of the following circles & sketch the graph of the circle. a) x 2 + y 2 = 1 b) x 2 + ( y - 3) 2  = 4 Solution In all of these

Solids, a can of soup is shaped like wich solid

a can of soup is shaped like wich solid

Fermats last theorem, Explain Fermats Last Theorem? How to solve problems u...

Explain Fermats Last Theorem? How to solve problems under Fermats Last Theorem?

Estimate the rms value and prominent features, Figure shows the auto-spect...

Figure shows the auto-spectral density for a signal from an accelerometer which was attached to the front body of a car directly above its front suspension while it was driven at 6

Numertic methods, solve by factorization method; 10x-6y-3z=100, -6x+10y-5z=...

solve by factorization method; 10x-6y-3z=100, -6x+10y-5z=100, -3x-5y+10z=100

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