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

Shares and dividend, A man in rested rupee 800 is buying rupee5 shares and ...

A man in rested rupee 800 is buying rupee5 shares and then they are selling at premium of rupee 1.15.he sells all the share.find profit?

Comparison test or limit comparison test, Comparison Test or Limit Comparis...

Comparison Test or Limit Comparison Test In the preceding section we saw how to relate a series to an improper integral to find out the convergence of a series.  When the inte

Linear Programming, #question.A manufacturer produces two items, bookcases ...

#question.A manufacturer produces two items, bookcases and library tables. Each item requires processing in each of two departments. Department 1 has 40 hours available and departm

Ways for 30 identical balls can be distributed among 4 boys, In how many w...

In how many ways 30 identical balls can be DISTRIBUTED among 4 boys?? Ans) Let they get a,b,c,d respectively. You requireto find the non negative integral results of a+b+c+d=3

Developing an understanidng of multiplication, DEVELOPING AN UNDERSTANIDNG ...

DEVELOPING AN UNDERSTANIDNG OF MULTIPLICATION :  The most important aspect of knowing multiplication is to understand what it means and where it is applied. It needs to be first i

find the original number, A two-digit number is seven times the sum of its...

A two-digit number is seven times the sum of its digits.  The number formed by reversing the digits is 18 less than the  original number. Find the original number.

Subtraction involving negative numbers, Q. Subtraction Involving Negative N...

Q. Subtraction Involving Negative Numbers? In order to subtract positive and negative numbers, you need to be aware of the Rule for Subtraction. This rule states that subtracti

Multiple integrals, how to convert multiple integral into polar form and ch...

how to convert multiple integral into polar form and change the limits of itegration

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