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

#title.heat loss in a cylindrical pipe., briefly explain how the famous equ...

briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived

What is the greatest value of the number, Five more than the quotient of a ...

Five more than the quotient of a number and 2 is at least that number. What is the greatest value of the number? Let x = the number. Notice that quotient is a key word for div

.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

Evaluate following. 0ln (1+)excos(1-ex)dx substitution, Evaluate following....

Evaluate following. ∫ 0 ln (1 + π )   e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get

Area, find area of rectangles and triangles put together

find area of rectangles and triangles put together

How to calculate probability of event, Q. How to calculate Probability of e...

Q. How to calculate Probability of event? Ans. What chance do I have to toss the coin and get a head? You might think 50-50, 50%. What about tossing it 5 times and getting

Determine the transfer function, A digital filter has zero at z=a and poles...

A digital filter has zero at z=a and poles at z=b andz=c, where a, b, c are the real constants. Determine the transfer function and the frequency response function of the filter an

Algorithm, what does algorithm refer to

what does algorithm refer to

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