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

Calculate the mean, Calculate the mean, variance & standard deviation of th...

Calculate the mean, variance & standard deviation of the number of heads in a simultaneous toss of three coins.     SOLUTION:    Let X denotes the number of heads in a simu

Binomial mathematical properties, Binomial Mathematical Properties 1. ...

Binomial Mathematical Properties 1. The expected or mean value = n × p = np Whereas; n = Sample Size p = Probability of success 2. The variance = npq Whereas; q =

Find relation between x and y while lies on straight line, Find the relatio...

Find the relation between x and y when the point (x,y) lies on the straight line joining the points (2,-3) and (1,4) [ Hint: Use area of triangle is 0] Ans :   Hint: If the poi

Dividing, I don''t know how to do the next step like if I had 73 divided by...

I don''t know how to do the next step like if I had 73 divided by 9 wouldn''t 7 go into nine 1 time then you have to do something else but that is the part I don''t understand

Exponents, how to solve this question:(2x)5*(2x)-4*(2x)-3*(2x)6

how to solve this question:(2x)5*(2x)-4*(2x)-3*(2x)6

Word Problem, a local pizza store offers medium two-topping pizzas delivere...

a local pizza store offers medium two-topping pizzas delivered for $6.00 per pizza plus a $1.50 delivery charge per order. on weekends, the store runs a game day special: if six or

Mass marketing, is mass marketing completely dead?

is mass marketing completely dead?

Sequencing., how to select out time for m2

how to select out time for m2

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