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

Doubles Plus 1 and Doubles Minus 1, Write the doubles fact you used to solv...

Write the doubles fact you used to solve the problem. 7 + 8 = 15

Find the number of zeros of the polynomial, Find the number of zeros of the...

Find the number of zeros of the polynomial from the graph given. (Ans:1)

Expected value of perfect information, Expected Value of Perfect Informatio...

Expected Value of Perfect Information In the above problems we have used the expected value criterion to evaluate the decisions under the conditions of risk. But, as long as un

Example of elps maths learning, Do you agree with the necessity of the sequ...

Do you agree with the necessity of the sequencing E - L - P - S for learning? If not, then what do you suggest as an alternative path for understanding and internalising mathematic

Bcubi bui, hellow my name is isa soo what is your name?? i love the name ex...

hellow my name is isa soo what is your name?? i love the name experts mind so what is 8000+98800+600+935=what i do not know so can you tell me thank you oh thir is another one wha

Poisson mathematical properties, Poisson Mathematical Properties 1. Th...

Poisson Mathematical Properties 1. The expected or mean value = np = λ Whereas; n = Sample Size p = Probability of success 2. The variance = np = ? 3. Standard dev

Find the area of triangle, Find the area of TRIANGLE ? To find the area...

Find the area of TRIANGLE ? To find the area of a triangle, multiply the base (b) by the height (h), and divide the resulting number in half. In other words, area is. It is

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