Required information NOTE: This is a multi-part question....

Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine whether these posets are lattices. ({1, 3, 6, 9, 12}, |)

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00:01 So we have two posets here, we want to see what additional structure they have.

00:05 Whether they're lattice, complemented lattice, or boolean algebras.

00:11 Something we see here, they are actually both lattices.

00:15 It's a bit tedious to verify this, but you can do it through brute force or just kind of by eyeballing it.

00:22 You see for example d and f join at a and meet at g.

00:27 E and c also join at a and meet at g, and so on and so forth.

00:33 B, it's a little bit harder to see that it is a lattice, but it is in fact still a lattice.

00:38 D and g for instance join not till a and meet at h.

00:46 Is that right? that is right.

00:51 That's good, they are both lattices and we can check that through brute force.

00:55 Are they complemented lattices though? i'm going to claim that no they are not.

01:00 For example, in part a, what would be the complement of d? well if we do the meets here, a and d of course meet at a, as do c and b, which is good.

01:13 E, f, and g each though meet at d because they are less than d.

01:18 And their joins, excuse me, those are the joins, i always get this mixed up.

01:24 The meets, a and d meet at d.

01:28 C and b respectively at f join respectively to f and f at e...

Question

Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine whether these posets are lattices. ({1, 3, 6, 9, 12}, |)

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