Complemented Lattice

Discrete Mathematics: Complemented Lattice
Topics discussed:
1) Complemented lattice.
2) Finding if the given lattice is a complemented lattice or not.

Music:
Axol x Alex Skrindo - You [NCS Release]

#DiscreteMathematicsByNeso #DiscreteMaths #PartialOrdering #Lattice

[sandeepmukherjee]

Homework Problem 11:30
a complemented lattice as every element has a complement

[Akhilesh]

In the homework question we can clearly see that it is a bounded lattice because the least element = a and greatest element = e.
Now complement of b is c as well as d because LUB(b, c) = e and GLB(b, c) = a. And LUB(b, d) = e and GLB(b, d) = a.
Similarly complement of d is b as well as c. And complement of c also exists.
Complement of a is e and complement of e is a.

We can see that complement of every element exist.
Therefore it is a complemented lattice.

[bansarikikani]

your videos helps a lot during university exam. Its a quick review of a chapter or a topic. very well explained and very simplified to understand. Thank you, we appreciate your lectures.

[rajeshprajapati]

Answer to H.W. 11:30

GE = e and LE = a so Bounded Lattice.
Comp(GE) = LE and Comp(LE) = GE => Comp(a) = e and Comp(e) = a
Also, Comp(b) = d then Comp(d) = b
Also, Comp(c) = e
So, Complement of every elements exists. Therefore, given Hasse Diagram is Complemented Lattice.

[rajeshprajapati]

Good Luck for 2022 Neso Team. Keep on making such interactive videos. Thanks for the amazing work.

[hewadewageashan]

Home work is a complemented lattice because every element has a complement

[normanhenderson]

You have explained the logic behind these relationship.

[directionerformonthsandmore]

Your videos really helped clear my concepts. Thank you.

[hirakhan]

Yes it is a bounded and complemented lattice 🫶

[pranavgor]

THANK YOU A LOT OF CAUSE TOMMORROW S MY EXAM AND YOUR VIDEO HAS CLEAR MY EVERY DOBUT THANKS A LOT SIR

[sathviknandeesha]

Sir if we get to know for a single element that there exists no complement can we conclude it by explaining for a single element itself or should we show all the other possibilities.

[ilovescience]

But What About E? Gave me such a good laugh lol thanks

[marcfruchtman]

Thanks for the video. It would be helpful to include why complemented lattices are useful in the video.

[Vishal-vzer]

yes last lattice is boundend becase there is greatest element and least element, and is complemented lattice because c is complement of b and d

[niteshtiwari]

Yes, it is a bounded lattice as well as it is a complemented lattice.

[Anirudh_Srinivasan]

Homework question. The given lattice is a bounded lattice and also a complemented lattice.

[troopergaming]

Answer - it is bounded as well as complemented lattice

[SumedhLohekar]

yes its a complimented lttice mere exam mein aaya tha ye question

[ShibashankarBarik-zt]

last questions have complemented lattice

[MilanSabKarlega]

Yrr itne ache lecture me kitne Kam views ate he, koi padhta likhta ni he kya 🥲