Solution to 1) Draw the Hasse diagram for inclusion on the set P(S), where S = {a, … - Sikademy
Author Image

Archangel Macsika

1) Draw the Hasse diagram for inclusion on the set P(S), where S = {a, b, c, d} 2) Let S = {1,2,3,4} with lexicographic order "<=" relation a. Find all pairs in S x S less than (2, 3) b. Find all pairs in S x S greater than (3, 1) c. Draw the Hasse diagram of the poset (S x S, <)

The Answer to the Question
is below this banner.

Can't find a solution anywhere?


Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Part 1 and 2

Part a

(2, 2), (2, 1),(1, 4), (1, 3), (1, 2), (1, 1)

Part b

(3, 2), (3, 3),(3, 4), (4, 1), (4, 2), (4, 3), (4, 4)

Part c

P(A) = \big \{ \varnothing, \{a\}, \{b\}, \{c\}, \{a, b\}, \{b, c\}, \{a,c\}, \{a, b,c\} \big \}.

Let's show S=(P(A), \subseteq) is a poset. Let's show that S satisfies the following three properties.

  1. Reflexivity. For every x \in P(A) \ x \subseteq x is trivially true.
  2. Antisymmetry. Let x, y \in P(A) and x \subseteq y \wedge y \subseteq z.Then x=y from the definition.
  3. Transitivity. Let x, y,z \in P(A) and x \subseteq y \wedge y \subseteq x. Then for alla \in x we have a \in y, and therefore a \in z. Thus x \subseteq z.

The Hasse diagram for (P(A), \subseteq) is shown below.

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-2701-qpid-1171