partial order

Let F be the set of all functions from {1,..., n} to {0,1}. Define the binary relation ≤ on F as follows: ∀f,g∈F, f≤ g if and only if ∀x ∈ {1, ..., n}, f(x) ≤ g(x), where 0 ≤ 1. Wh...

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 set $X = \{a,b,c,d,e\}$ under the partial ordering $R = \{(a,a), (a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e), (c,c), (c,e),(d,d),(d,e),(e,e)\}$. The Hasse diagram of the...

A partial order P is defined on the set of natural numbers as following. Herw x/y denotes integer division. i) (0, 0) $$ \in \,P$$. ii) (a, b) $$ \in \,P$$ if and only a % $$10\, \...

The inclusion of which of the following sets into S = { {1, 2}, 1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5} } Is necessary and sufficient to make S a complete lattice under the...

Let $$X$$ $$X = \left\{ {2,3,6,12,24} \right\}$$. Let $$ \le $$ the partial order defined by $$x \le y$$ if $$x$$ divides $$y$$. The number of edges in the Hasse diagram of $$\left...