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

Mensuration of plane figures, a sail has a spread of canvas as measured 12'...

a sail has a spread of canvas as measured 12'',12'', 15'' and 9'' and it has 90 degrees. Find the area of one side of the sail

Pharmacy technician, Tetracycline 500 mg capsules Sig: 1 cap po bid for 14...

Tetracycline 500 mg capsules Sig: 1 cap po bid for 14 days. Refills: 2 What is the dose of this medication:____________________ (0.5 point) How many doses are given per day:______

Systems of equations revisited, Systems of Equations Revisited We requ...

Systems of Equations Revisited We require doing a quick revisit of systems of equations. Let's establish with a general system of equations. a 11 x 1 + a 12 x 2 +......

Gravity, There is a list of the forces which will act on the object. Gr...

There is a list of the forces which will act on the object. Gravity, F g The force because of gravity will always act on the object of course. Such force is F g   = mg

Laws of set algebra, Laws of Set Algebra From the given Venn diagram w...

Laws of Set Algebra From the given Venn diagram where T is the universal set and A its subset that we can deduce a number of laws as: i. A υ Ø = A ii. A υ T = T

Rate and ratio, express 4:24 as fraction in lowest term

express 4:24 as fraction in lowest term

Value of perfect information, Value of perfect information This relates...

Value of perfect information This relates to the amount that we would pay for an item of information such would enable us to forecast the exact conditions of the market and act

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