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2

And here is more simple definition than @egregs ooalign: \def\gdw{\mathrel{{>}\mkern-13mu{<}}} $A \gdw B$ And it is optical better:

5

This is the unicode U+2AA4 named "GREATER-THAN OVERLAPPING LESS-THAN". Here, you may see, which fonts support this symbol and here, which fonts on your system do provide it. The MWE requires Lua- or XeLaTeX. It just shows two fonts I found on my PC. Of course, you should define your preferred version in a \mathrel-command. % arara: lualatex ...

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Here is a nice introduction I found to drawing Venn diagrams: http://users.ju.edu/hduong/math220/venn_diagrams.pdf I put it here, since this question is one of the first results google gives when looking for "how to draw Venn diagrams" (naturally), and also other places refer here, but I feel none of the answers give an introduction to drawing Venn ...

0

There is a difference. Here are 5 versions of your formula, with the normal spacing, and adding \,, \:, \; and \. In my opinion, the only places that might justify adding some space are just between the quantifiers. For the parentheses and the binary symbol, spacing is fine: \documentclass{article} \usepackage{mathtools} % \begin{document} \begin{gather*} ...

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Can't see any problem here. Does none of these work for you? Just in order to give some examples. You can find a big list here. % arara: pdflatex \documentclass{article} \usepackage{mathtools} \newcommand*{\test}[1]{$G#1(\forall(x)#1\forall(y)#1(p(x)#1\vee#1\neg{}p(y)))$\par} \begin{document} \test{} \test{\,} \test{\>} \test{\ } \test{\mkern+10mu} ...

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