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

Prove that cos - sin = v2 sin , If cos?+sin? = √2 cos?, prove that cos? - ...

If cos?+sin? = √2 cos?, prove that cos? - sin? =  √2 sin ?. Ans:    Cos? + Sin? =  √2 Cos? ⇒ ( Cos? + Sin?) 2  = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒

Angles, how to measure missing angle of an adjacent angle

how to measure missing angle of an adjacent angle

Volumes of solids of revolution - method of rings, Volumes of Solids of Rev...

Volumes of Solids of Revolution / Method of Rings In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of rev

Right angle triangle, If the points for a right angle triangle are XYZ wher...

If the points for a right angle triangle are XYZ where do I mark the points?

Probability, the probability that an account officer will pass her exam is ...

the probability that an account officer will pass her exam is 5/9. if she pass,the probability that she will be promoted is 3/4. she is not promoted if she fails her professional e

What is the length of one side of the square, The area of a square is 64 cm...

The area of a square is 64 cm 2 . What is the length of one side of the square? To find out the area of a square, you multiply the length of a side through itself, because all

Mean value theorem function, Mean Value Theorem : Suppose f (x) is a funct...

Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on

Solving whole-number riddles, I am greater than 30 and less than 40. The su...

I am greater than 30 and less than 40. The sum of my digits is less than 5. who am I?

Experiments probabillity of compound events, what is the expiremental proba...

what is the expiremental probability that the next toss and spin will result in 3 and tail if 1-heads,53.2-heads,49.3-heads,54.1-tail,65.2-tails,71.3-tails,62

Find fourier series, Question: Find Fourier series for the periodic fun...

Question: Find Fourier series for the periodic function of period 2 π,defined by      f(x) = x 4 ,  - π ≤ x ≤ π

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