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

Addition and subtraction of rational expressions, Now come to addition and ...

Now come to addition and subtraction of rational expressions.  Following are the general formulas.  (a/c) + (b/c) = (a + b)/c

the system by graphing, Suppose you are in the market for a new home and a...

Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative later shows that there

Cylinder, #question Show that the enveloping cylinder of the conicoid ax 2 ...

#question Show that the enveloping cylinder of the conicoid ax 2 + by 2 + cz 2 = 1 with generators perpendicular to the z-axis meets the plane z = 0 in parabolas

Pair of straight line, The equation ax2 + 2hxy + by2 =0 represents a pair o...

The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+

Define euler circuit and euler path, Define Euler Circuit and Euler Path.  ...

Define Euler Circuit and Euler Path.  Which of the following graphs have an Euler circuit and Euler path.

Student, What is the slope and y intercept for (6,5) (-3,8)

What is the slope and y intercept for (6,5) (-3,8)

Linear algebra, solve for k such that the system 4x+ky=6 kx+y=-3

solve for k such that the system 4x+ky=6 kx+y=-3

Help, dividing decimals

dividing decimals

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