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

Phase plane, Before proceeding along with in fact solving systems of differ...

Before proceeding along with in fact solving systems of differential equations there's one topic which we require to take a look at. It is a topic that's not at all times taught in

What are mutually exclusive events, Q. What are Mutually Exclusive events? ...

Q. What are Mutually Exclusive events? Mutually Exclusive Events are mutually exclusive if they cannot occur at the same time. For example, if you roll one die, you canno

Radicals, We'll include this section with the definition of the radical.  I...

We'll include this section with the definition of the radical.  If n is a +ve integer that is greater than one and a is a real number then, Where n is termed as the index,

What is inductive reasoning, What is Inductive Reasoning ? Sometimes we...

What is Inductive Reasoning ? Sometimes we draw conclusions based on our observations. If we observe the same results again and again, we conclude that the event always has the

.probability, a box contains 4 white and 6 green balls.Two balls are drawn ...

a box contains 4 white and 6 green balls.Two balls are drawn randomly with replacement.Show the probability on tree dig.

The definition of the derivative, The Definition of the Derivative : In t...

The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the ins

Linda bought 35 yards of fencing how much did she spend, Linda bought 35 ya...

Linda bought 35 yards of fencing at $4.88 a yard. How much did she spend? To multiply decimals, multiply generally, count the number of decimal places in the problem, then us

PDE, Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ...

Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket

UNITARY METHOD, A group of 120 men had food for 200 days.After 5 days , 30 ...

A group of 120 men had food for 200 days.After 5 days , 30 men die of disease.How long will the remaining food last

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

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