Recent questions tagged partial-order

1
If $f(x,y)=x^{3}y+e^{x},$ the partial derivatives, $\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y}$ are $3x^{2}y+1, \: x^{3}+1$ $3x^{2}y+e^{x}, \: x^{3}$ $x^{3}y+xe^{x}, \: x^{3}+e^{x}$ $2x^{2}y+\dfrac{e^{x}}{x}$
2
A partial ordered relation is transitive, reflexive and antisymmetric bisymmetric antireflexive asymmetric
3
​ Let $N=\{1,2,3,\dots\}$ be ordered by divisibility, which of the following subset is totally ordered? $(2,6,24)$ $(3,5,15)$ $(2,9,16)$ $(4,15,30)$
4
what is the least upper bound of {a, b, c}?
5
What is dual of a POSET?
6
Let Q denote the set of rational numbers and S = {x | x belongs N ; N; x>=10} Consider the Following POSETs I. (Q ∩ [0, 1], ≤) II. (S, ≤) Which of the above POSETs are well ordered?
1 vote
7
If $u=f(y-z, \: \: z-x, \: \: x-y)$, then $\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} + \frac{ \partial u}{ \partial z}$ is equal to: $x+y+z$ $1+x+y+z$ $1$ $0$
8
If $w=f(z)=u(x,y)+i \: v(x,y)$ is an analytic function, then $\frac{dw}{dz}$ is: $\frac{ \partial u } {\partial x}- i \frac{ \partial u}{\partial y}$ $\frac{ \partial u } {\partial x}+ i \frac{ \partial v}{\partial y}$ $\frac{ \partial u } {\partial x}- i \frac{ \partial v}{\partial x}$ $\frac{ \partial u } {\partial x}+ i \frac{ \partial u}{\partial y}$
9
The general solution of the partial differential equation $(D^2-D’^2-2D+2D’)Z=0$ where $D= \frac{\partial}{\partial x}$ and $D’=\frac{\partial}{\partial y}$: $f(y+x)+e^{2x}g(y-x)$ $e^{2x} f(y+x)+g(y-x)$ $e^{-2x} f(y+x)+g(y-x)$ $f(y+x)+e^{-2x}g(y-x)$
10
The set of all English words ordered in a dictionary is ________ $A)$ not a poset $B)$ a poset but not totally ordered $C)$ a totally ordered set but not well ordered $D)$ a well ordered set
11
Is 1 a lattice?
1 vote
12
Which of the following statements is true? $(Z, \leq)$ is not totally ordered The set inclusion relation $\subseteq$ is a partial ordering on the power set of a set S $(Z, \neq)$ is a poset The directed graph is not a partial order
13
How is this a lattice?