Total Order

Let P be the partial order defined on the set {1,2,3,4} as follows P = {(x,x) | x ∈ {1,2,3,4}} ∪ {(1,2), (3,2), (3,4)} The number of total orders on {1,2,3,4} that contain P is ___...

Let $P$ be the partial order defined on the set {1,2,3,4} as follows: $P = \{(x, x) \mid x \in \{1,2,3,4\}\} \cup \{(1,2), (3,2), (3,4)\}$ The number of total orders on {1,2,3,4} t...

Consider the following relation on subsets of the set S integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric diff...