Lattice

Discrete Mathematics: Lattice
Topics discussed:
1) The definition of Lattice.
2) Identifying if the given Hasse Diagram is a Lattice.
3) Identifying if the given Poset is a Lattice.
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Music:
Axol x Alex Skrindo - You [NCS Release]
#DiscreteMathematicsByNeso #DiscreteMaths #PartialOrdering #HasseDiagram

[@_PAYALGAIKWAD]

all videos are arranged so well in a proper sequence

[@trusttheprocess4775]

Fantastic videos. These videos are alone going to help me pass maths this semester.

[@nins1709]

Thank you so much. Your one lecture clears all my doubts about the lattice topic

[@benalbritton]

FYI, you don't call the symbol for the empty set "phi". Phi is a greek letter that looks a little similar to the symbol for the empty set, but mathematicians are not using the greek letter phi in this case, it is just it's own symbol that denotes the empty set.

[@AkamiChannel]

Yeah that was surprising for such a well-presented and informative video to make this error

[@barlog6679]

wouldn't b GLB(f,g) = e?

[@agnidebmukherjee9756]

Yes true..

[@agnidebmukherjee9756]

@@adityanprakash1281 not at all

[@csbytes137]

Same doubt

[@barlog6679]

i figured it out, the elements that can be GLB in (f,g) are e and b. Since you cannnot determine whether e is greater than b or b is greater than e due to the lack of relationship between e and b, there is no GLB. The same logic applies to determine the GLB and LUB of other pair of elements.

[@its_ayush7286]

@@barlog6679 thank you for pointing out my same question and also for giving the answer of it. That is something that i didn't know.

[@madapanameena1320]

From figure (a)
Consider the incomparable pair (d,g)
GLB(d,g)=f
LUB(d,g)=¢( null set)
So, this is not lattice.
I have doubt .. please clarify that.

[@adityaralhan1154]

Lub of d and g is g

[@pranavnyavanandi9710]

Please list the related playlist in the video description as well, it makes it much easier to navigate.

[@marcusmors8485]

Thank you, it was easy to understand and you set the previous knowledge requirements from the start.

[@ambikas4905]

Well explained,with more examples,there is no doubt n understand

[@ankitpanwar5032]

Thank you❤❤ neso academy, I grateful to for my sessional exams

[@rishabhm456]

Hi five bro 🤜

[@bj_ets8010]

You are a life saviour sir🔥💯💥

[@kashmirking2446]

Thank u so much sir.....all videos are in proper sequences

[@y.8901]

Hello, at 7:25 can we say that the lower bounds of (f,g) are b,e,c,a but since b and e are not comparable -> No upper bound ?

[@doesnotexist8873]

yes

[@rajeshprajapati6662]

Upper bound of (f,g) is h. There is no lower bound for (f,g). You should have written "No Lower Bound".

[@prithwihegde349]

​@@rajeshprajapati6662hey y e can't be considered as GLB?
Please could you explain...

[@chiragmehta2955]

sir your voice so soothing ..after hearing that it makes maths a very easy subject. thank u for ur hardwork.

[@yeongwooh4921]

GLB(f,g) for all pair isn't defined, thus the set is empty. since the two preceding lower bounds are incomparable, we can't define greatest lower bound.

[@wrath2801]

bhai tu IIT ka hai?

[@jordynbell02]

This video is absolutely amazing!

[@_PAYALGAIKWAD]

thanks a lot sir..Your videos are so easy to understand and organised...

[@praveenkumarchettiyar2695]

Thankyou sir you rescued me a day before exam 😊😅

[@DuongNguyen-en1pi]

6:12, example 2 (a), what is the GLB and LUB of pair (d and g)?

[@enes5345]

GLB d and LUB g

[@marah8158]

@@enes5345
couldn't be like this?
GLB is f
LUB is ø
how GLB is d when they first meet in f?

[@zeusbgmi6476]

This is somewhere excellence is found!

[@mahendrakergaurav5867]

thanks man,apppreciate your work

[@teneplays]

8:45 example 3 was the same as in my notebook

[@user-vk9vx8uk2p]

this guy is an amazing teacher omg

[@likithgannarapu8454]

at 8:15 in example(c) why didn't you consider (b,c) as incomparable????

[@rajeshprajapati6662]

You can consider it and you will find that unrelated pair (b,c) has GLB = a and LUB = g.

[@egehanyildiz]

sir in example (b) isnt GLB of f and g is a? By following the path downwards we can find a lowerbound

[@rajeshprajapati6662]

Lower bound of (f,g) - abce
Let's check for GLB :
a - All elements of LB related to a ? No [Using Hasse Diagram]
b - All elements of LB related to b ? No [Using Hasse Diagram]
c - All elements of LB related to c ? Obviously No [Using Hasse Diagram]
e - All elements of LB related to e ? Obviously No [Using Hasse Diagram]
So, GLB = Phi

[@anushiya4453]

thanks man!@@rajeshprajapati6662

[@Akshay_pratap_singh_007]

Very well explanation Sir !!

[@saiyedasiddika3974]

It’s really helpful

[@satyamtiwari331]

fantastic explanation

[@arunsuresh8547]

In fig (c) why don't you consider f,e and d,c as incomparable pairs ?

[@osamansr5281]

what does the "rank" of a lattice mean? what's a "rank-1" lattice?

[@isai5813]

Please add python and Dynamic programming courses too

[@suhankrishna4567]

i will pass because of you. god bless you!

[@bbmathematics224]

Excellent method..❤

[@sidrahwaris7885]

thank u so muchhhh very helpfullll!!!!!!!

[@engineerguruji2]

Thanks so much

[@brainexercise1234]

Nice explanation

[@pahadiraishgamer1777]

Very helpfull

[@Bbdu75yg]

Amazing !🎉🎉🎉🎉

[@bhaktikhokad7113]

nice expalined properly

[@kasiiragavarapu673]

At 6:17 why don't we consider (g, d) to check either they have glb and lup

[@doesnotexist8873]

because d is related to g through transitive property

[@engineerguruji2]

Good morning every one

[@shivanikj3047]

Thank you 😃

[@Kuldeepsingh.]

great video sir

[@leonthethird7494]

You're a legend

[@lloydmoore6507]

Doesn't 3 also divide 12?

[@aaravjayalwal3416]

Way better than nptel

[@nehakhanolkar3861]

Can someone please explain what do we mean by 'incomparable elements '.

[@nileshmishra5482]

It means if neither aRb nor bRa..

[@parmeshwariswami3530]

Sir ji direct product of lattice explain videos

[@amruta2114]

Thku

[@AnushkaSingh-sl3zn]

b,c ???

[@shankarpubg9413]

Wow 😲

[@sabrinahhewitt119]

Love🎉

[@noelomidze2079]

კიუელები გამოჩნდით xd

[@08_it_aditkumar15]

Wtf?

[@arunsuresh8547]

In fig (c) why don't you consider f,e and d,c as incomparable pairs ?