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

Measures of central tendency-computation method, Computation method   ...

Computation method           Whereas L = Lower class boundary of the class having the mode             f 0 = Frequency of the class below the modal class

What is congruent angles in parallel lines, What is Congruent Angles in Par...

What is Congruent Angles in Parallel Lines ? Postulate 4.1 (The Parallel Postulate) Through a given point not on a line there is exactly one line parallel to the line. T

NCCER, what is 9/16 Divided by 7/8

what is 9/16 Divided by 7/8

Without a calculator give the exact value, without a calculator give the ex...

without a calculator give the exact value of each of the following logarithms. (a) (b) log1000 (c) log 16 16 (d) log 23 1  (e)  Solution (b) log10

Differentiation, Need Solution Find (dy)/( dx) for; (i). y = x 7 ...

Need Solution Find (dy)/( dx) for; (i). y = x 7 (ii). y = x 2γ (iii). y = x -3 (iv). y = x

Evaluate algebraic word problems, Evaluate algebraic word problems: A ...

Evaluate algebraic word problems: A utility has three nuclear facilities which supply a total of 600 megawatts (Mw) of electricity to a particular area.  The largest facility

Factoring trinomial, what is the factor of the trinomial 2x2-7x-4

what is the factor of the trinomial 2x2-7x-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