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

Facts regarding linear equations, To solve out linear equations we will mak...

To solve out linear equations we will make heavy use of the following facts. 1. If a = b then a + c = b + c for any c.  All it is saying that we can add number, c, to both sides

Rates of change and tangent lines in limits, Rates of Change and Tangent Li...

Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.

Algebra, how do you solve quadratic equations by factoring?

how do you solve quadratic equations by factoring?

Combining like terms, i don''t understand what my teacher when she talks ab...

i don''t understand what my teacher when she talks about when she talks about cosecutive integers etc... so can u help me???

Ratio lanquage, Alexis needs to paint the four exterior walls of a large re...

Alexis needs to paint the four exterior walls of a large rectangular barn. the length of the barn is 80 feet the width is 50 feet and the height is 30 feet. The pain costs 28 dolla

Find relative extrema f ( x ) = x2 on [-2, Recognizes the absolute extrema...

Recognizes the absolute extrema & relative extrema for the given function.  f ( x ) = x 2        on                  [-2, 2] Solution Following is the graph for this fun

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