Parial Order and Hasse Diagram
A poset or partially ordered set A is a pair, ( B, preceq ) of a set B whose elements are called the vertices of A and obeys following rules
___ elements of A are those where a preceq c in A does not contain elements in c
Let A={1,2,3,4,6,24,36,72}, Let preceq be the partial order defined by A preceq B if a divides b. Number of edges in the Hasse diagram of (A,preceq) is
If A = {1, 2, 3, 6, 9, 18], then number of edges in the poset diagram of poset [A; /] is
Let P be the set of all people. Let R be a binary relation on P such that (a, b) is in R if a is a brother of b. Is R symmetric, transitive, an equivalence relation, a partial order relation?
Which of these is a valid Hasse diagram property?
In the power set P({1,2,3}) ordered by set inclusion (⊆), how many incomparable pairs of elements are there?
Which statement about lattices is true?
Given a finite partially ordered set (P,≤), what is the relationship between its minimal elements and maximal antichains?