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

Applications of markov chains in business, please help me in my assignment,...

please help me in my assignment, explain Applications of Markov Chains in Business.

Determine the permutation, There are 6 contestants for the post of chairman...

There are 6 contestants for the post of chairman secretary and treasurer. These positions can be filled by any of the 6. Find the possible no. of ways whether the 3 positions may b

Find the derivations of functions, Find the derivatives of each of the foll...

Find the derivatives of each of the following functions, and their points of maximization or minimization if possible. a.  TC = 1500 - 100 Q + 2Q 2 b.  ATC = 1500/Q - 100 +

Concrete to abstract-how mathematical ideas grow, Concrete to Abstract :  ...

Concrete to Abstract :  Mathematics, like all human knowledge, grows out of our concrete experiences. Let us take the example of three-dimensional shapes. Think about how you came

What is the probability of tossing a head, Q. What is the probability of to...

Q. What is the probability of tossing a head? List the sample space for tossing a coin once. What is the probability of tossing a head? Solution:  If you tossed a coin once

Find the probability, Q. Suppose Jessica has 10 pairs of shorts and 5 pair...

Q. Suppose Jessica has 10 pairs of shorts and 5 pairs of jeans in her drawer. How many ways could she pick out something to wear for the day? What is the probability that she pick

Find the 14th term in the arithmetic sequence. 60, Find the 14th term in t...

Find the 14th term in the arithmetic sequence. 60, 68, 76, 84, 92

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