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I found this post, which explains orthogonal and not orthogonal symbols.

I was able quickly to find the orthogonal symbols as \perp, \upvdash etc., but not able to find a top line which strikes the sign from the top left to bottom right. One idea is to combine to symbols e.g., use one of the aboves and add the line in top of it. However I don't know how to do it.

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I'm not sure if I understood your question correctly, but if you want to negate \perp, just add \not before it, e.g., \not\perp. I hope it helps. – Paulo Cereda Sep 6 '11 at 11:03
I fully agree with that answer: addiction to symbols is dangerous; and \not\perp doesn't seem very useful to me. – egreg Sep 6 '11 at 11:18
@egreg Why is addiction to symbols dangerous? – N.N. Sep 6 '11 at 15:27
@N.N. I'll repeat what I said in chat. As a young aspiring mathematician I was fond of symbols and overused them; experience showed me that less symbols and more words may make the exposition clearer. In some papers one can find newly created symbols that are used only a couple of times: these are obvious signs of "symbol addiction". As another example, long descriptions of sets with X={x\in U:...} may almost always be improved by saying the set $X$ consisting of elements $x\in U$ such that ... – egreg Sep 6 '11 at 15:39
In writing, you'll probably be better off being clear and using words, not symbols. – lhf Jul 4 '12 at 11:13
up vote 14 down vote accepted

To negate the \perp (perpendicular) symbol, the command \not\perp provides a simple solution, but this negated symbol doesn't look that great IMHO:

enter image description here

If you load the mathabx package, however, you get the command \notperp which looks pretty good, as does now the output of \not\perp. The same effect can be achieved if you load the mnsymbol package and use its command \notperp. Notice, though, that even if you load the mnsymbol package, the output of \not\perp still looks pretty bad, viz., the same as if you didn't load any extra package at all.

Addendum: Following a request by the OP, here's an MWE that shows how to load the mathabx package and generate the symbol using the package's \notperp macro:

$a \not\perp b$, $c \notperp d$

enter image description here

Alternatively, here's an MWE showing the use of the MnSymbol package to generate these symbols:

$a \nperp b$, $c \not\perp d$

enter image description here

Happy TeXing!

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Cannot load mathabx; LaTeX Error: Command `\corresponds' already defined. Show a simple example how you do it! – user44967 Sep 9 '11 at 5:24
@user44967: The style used in your comment could easily be misunderstood to be a little harsh and demanding. You probably didn't mean it as such, but the imperative paired with the exclamation mark are a bit off-putting. Maybe a better way to phrase a request for clarification would be "Could you show a simple example of how to use your solution?". – Jake Sep 9 '11 at 11:30
SORRY! Could you show a simple example of how to use your solution? and ... THANKS for your help – user44967 Sep 9 '11 at 12:09
@user44967: I trust that the two MWEs I've provided in the meantime meet your needs. – Mico Sep 9 '11 at 13:14

You can add a \not in front of it:

a \not\perp b

This gives you a struck through orthogonal symbol.

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