skew unequal symbols

Question

Suppose I arrange the numbers 40, 30, 20, 10 in the corner positions of a 3*3 array. To be precise, the number 40 (resp. 30, 20, 10) is located at the top-left (resp., bottom-left, top-right, bottom-right) corner. I have 3 questions:

Q1. How to type a symbol at the left-middle position to indicate that 40 is larger than or equal to 30? I think the symbol looks like of shape "V" together with a vertical bar aside (at the left or right side of the shape "V").

Q2. How to type a symbol in the middle position of the array to mean that 40 is larger than or equal to 10? I imagine that it appears like a skew "V" with it mouth pointing to 40, and with a bar aside again.

Q3. How to type a single symbol at the middle position, meaning that "40 is larger than or equal to 10, and 30 is larger than or equal to 20"? I hope it looks like a brute-force combination of the symbol from Q2 and its analog.

I need these folk math symbols in a beamer presentation. Wish someone kindly give me a collection of feasible TeX codes to do them, so that I can learn how to make such symbols in TeX. Or, are there ready-made codes in any TeX packages? Thanks in advance!

Here is an MWE:

Thanks Henri. Here is an MWE:

\documentclass{amsart}
\begin{document}
\[
\begin{array}{ccc}
40 & > & 20\\
Q1 & Q2/Q3 & *\\
30 & > & 10
\end{array}
\]
\end{document}

Answer 1

To answer Q1 and Q2, with the help of \rotatebox from graphicx you can define two new commands:

\newcommand{\rotgeq}{\mathrel{\text{\rotatebox[origin=c]{-90}{$\geq$}}‌}}
\newcommand{\rotmedgeq}{\mathrel{\text{\rotatebox[origin=c]{-45}{$\geq$}}​}}

MWE

\documentclass{article}

\usepackage{amsmath}
\usepackage{graphicx}

\newcommand{\rotgeq}{\mathrel{\text{\rotatebox[origin=c]{-90}{$\geq$}}‌}}
\newcommand{\rotmedgeq}{\mathrel{\text{\rotatebox[origin=c]{-45}{$\geq$}}​}}

\begin{document}
\renewcommand{\arraystretch}{2} 
\[
\begin{array}{ccc}
  40      & \geq       & 20 \\
  \rotgeq & \rotmedgeq & \rotgeq \\
  30      & \geq       & 10
\end{array}
\]
\end{document} 

Output:

About your Q3, it could be feasible, but it would result in an unintelligible symbol, so I suggest you not to use a similar thing.

Answer 2

I would not recommend to overlay two symbols. This will confuse the reader. You may help a bit by putting lines between your entries. Here is an example using XY-pic in order to give you an idea of what I mean:

% arara: pdflatex

\documentclass{amsart}
\usepackage{graphicx}
\newcommand{\rotgeq}[1]{\text{\rotatebox{#1}{$\geq$}}‌}
\usepackage[all]{xy}

\begin{document}
\xymatrix{%
40 \ar[dd] _{\geq} \ar[rr] ^-{>} \ar[ddrr]  ^-(.75){\rotgeq{-45}} |!{[dd];[rr]}\hole & & 20 \ar[dd] ^-{\ast} \\
& & \\
30 \ar[rr] _{>} \ar[uurr]  ^-(.75){\rotgeq{45}} & & 10
}
\end{document}