in Set Theory & Algebra edited by
269 views
2 votes
2 votes

Let $[P(S), \supseteq]$ be a partial order relation defined on $P(S),$ where $S = \{1,2,3,4\}. P(S)$ is the set of all subsets of $S.$ Which of the following is the join of $\{1,2\}, \{3,4\}?$

  1. $\{3,4\}$
  2. $\{1,2,3,4\}$
  3. $\varnothing $
  4. $\{1,2\}$
in Set Theory & Algebra edited by
269 views

1 Answer

3 votes
3 votes
Let $S$ be a set, then $[P(S),$ superset$]$ is a boolean lattice, in which $LUB$ is the same as Intersection, and $GLB$ is the same as union.

Let $S$ be a set, then $[P(S),$ subset$]$ is a boolean lattice, in which $LUB$ is the same as union, and $GLB$ is the same as intersection.

1 comment

So is the final answer option c??
0
0