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

Bits, What is the largest number (in decimal) that can be made with 6 bits?...

What is the largest number (in decimal) that can be made with 6 bits?

Npv, how to calculate the npv

how to calculate the npv

Geometry, RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS...

RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS, ST, AND RT

Curve tracing, How we calculate region for curve tracing

How we calculate region for curve tracing

Equivalent fractions and area models, Need two equal fractions multiply an...

Need two equal fractions multiply and divide 1/6 3/4 5/15 2/7 20/25 24/36 4/9

Vectors, The angles between three non-zero and non coplanar vectors a,b and...

The angles between three non-zero and non coplanar vectors a,b and c are α between b and c and β between c and a and γ between a and b. The vector u and v are defined by u=(aX

SURFACE AREA AND VOLUMES, Metallic spheres of radii 6 centimetre, 8 centime...

Metallic spheres of radii 6 centimetre, 8 centimetre and 10 centimetres respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

Differential equatoin, how to solve questions based on higher differential ...

how to solve questions based on higher differential equations

Arithmetic/Geometric Sequences and Binomial Expansion, Find the 35th term o...

Find the 35th term of the sequence in which a1 = -10 and the common difference is 4.

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