23. Lattice Introduction - Gate

This lecture introduces the concept of lattice and the operation meet and join. It also covers the method to check if partial order becomes a lattice

[clmk]

just watched a 2 hour lecture about this topic and was so confused thanks for clearing up my confusion awesome video

[Sanjaysingh-kkvc]

sir please make this type of useful videos on other subjects also explain everything in short and examples you give on each problem are best ...thank u again.

[mukilannayagam]

Super explanation... Make cleared... Thanks a lot....

[madhurimaburagohain]

Your videos are really helped me..Thank you so much. Awesome teaching skill. Keep making videos !!

[anujshany]

i just loved 3-4 mins in the vid i got my doubt cleared.... thank you :)

[michaelkk]

Great explanation, thanks a lot.
However in 9:40 I didn't understand why 'a' isn't the meet of {c, e}.
Can somebody please explain?

[vidyaholla]

I think you should make more of such videos. Like not only on Math, but also on different subjects.

[roshansingh]

Sir maja aa gya iss baar toh sets mei top karoonga

[shubhamnarayan]

concepts are explained in short and precise manner . Amazing stuff for underatanding and revising concepts . A big thumbs up man 👍

[bobhu]

Just for some clarification. When finding greatest lower bound, you have to find all possible candidates, which is easy to see from the hasse graph. But then to pick up the greatest one, you not only have to check the height(low/high) in the graph, but also need to make sure you come to an end where only two candidates remain and they two have clear partial relation. See 10:36 the last question choice (ii) I think the two circled indeed have LUB and GLB which are just themselves two. It's not a lattice because the two nodes in the same second line have lower bound candidates: the last two nodes. And since the last two nodes have no partial relations, they can not be compared upper or lower. Note that you can not say the one higher in the graph is greatest lower bound because you have to always take partial relations into consideration. Just personal understanding, anyone have any suggestions?

[SzechSauce]

Excellent explanation, many thanks!!!

[ankurgupta]

I think some misunderstanding with the concepts of least upper bound and greatest lower bound because if that is the case then what is the difference between upper bound and least upper bound. can you give me an example to satisfy the below statement?
Definition Assume that (U, <=) is a partial order and that A is a subset of U .
If there exists an element z belongs to U such that
• for all x belongs to A : x <= z
• for all x belongs to U : (for all x belongs to A : x <= z) => z <= y
then z is called least upper bound of A.

[jimnewton]

I didn't exactly understand the construction. Didn't you say something different than you wrote? For example, the lattice of subsets of {1, 2, 3}, you drew branches connecting {1, 2} with {1} and {2}. However empty set is also a subset of {1, 2}, yet that branch is missing. So EXACTLY what do the branches mean?

I think there must be some additional requirement for the existence of a branch other than that it represents where the relation is true.

[Iuzzzzzz]

10:30 Diagram (ii) it's not the same as the previous example is it? because this time, the 2 other nodes are above the one being compared. Previously, they were below. So doesn't the one in the current digram have a GLB?

[jiazhang]

In the last problem, if we call (iv) a lattice, we must have (iii) as a lattice, since the node on the top can be the LUB of the two nodes circled. Does anyone have any idea about this?

[akanshadixit]

Nice lecture sir. Please clarify at 3:48, how 2 becomes an upper bound? As i compare it with the logic explained by you, the only upper bound should be 6 since 2 & 3 are not comparable?

[pavankumar]

In 3:49, why 6 isn't upper bound?

[upplee]

What if I take elements {8, 12, 24} what is the upper bound for this?

[abdurramijraj]

in 9:22 why there is no lub and glb the lower bound might be a and upper bound might be e
explain it please

[김동민-odw]

Thank you for great lecture
But ive got confused at 6:38
How can this be a lattice?
If i pick (2, 4)
I guess upper bound is {24, 12, 8}, and LUB doesnt exist since 12 and 8 arent comparable.
At what point did i misunderstood?? Thanks.