Unfortunately if you were able to do this before, there is no way to do it now. Here is a link to the updated Help Article on all shortcuts in Docs: https://support.google.com/docs/bin/answer.py?hl=en&answer=179738

The best way to do it now is Alt+I to access the menu options and C

++Edit (thanks to anon for pointing out easier way to access menus now++

Made an edit to keyboard inputs above to go directly to the Insert menu, and updated the keyboard shortcut for special chars which was changed.

For Apple apps, make a text replacement for it:

https://support.apple.com/kb/PH18439

Other apps like MS Word have their own system for this in their menus.

This is an easy one, you can just set up a macro to execute that combination of keys, in order to do this:

1. Open Microsoft Word and (to make things easier to explain) open the document you are currently working on

2. On the ribbon menu go to the developer tab and on the group code select record macro

3. On the window that just opened, on the Macro name you have to choose the name for the macro, it will only work with common letters and numbers with no spaces so no symbols like dashes, periods or commas, for sake of simplicity and organization write down in the text box (without quotation marks): "SymbolTherefore", if later you want to add more symbols you would want to write first the word Symbol (respecting the caption after each word) followed by the symbol's name, the same would go for anything else like TableSizeCard, FormatTitleGreen, etc. just make sure to use general descriptive names^{Went a bit off-track.}

4. We will leave the assign macro last because it would save the macro without allowing us to change the other options first. The store macro in will allow you to choose whether you want to macro to be saved to be available for all documents (existing and new ones) or, if you open the drop-down menu, for a specific document, for this case choose the first one and make the macro available for all documents (should be selected by default)

5. Now write down a description for the macro, I suggest this (without quotation marks): "Symbol - Therefore (∴)"

6. Next, on the assign macro to section you have to choose the method you want the macro to be executed with, the button option will create a button on the quick access bar and the keyboard option will allow you to set a combination of keys to execute the macro, for this instance choose the keyboard option

   1. Button
      ^{This is the easy way to do it but it is also not very useful because you need to use your mouse to trigger it}
      This will open a window with two columns, on the left you have the macro you created and on the right column, it shows you the quick access bar icons you currently have, just double click the macro on the left to add it to the active list of buttons and save

   2. Keyboard
      After selecting this option the customize keyboard window will pop-up, here all you have to do is to click on the press new shortcut key box and proceed to do as it describes, I used the Alt + L combination but you can use whatever you want (hit enter to accept the new trigger), just make sure to confirm whether the key or combination of key is not already being used by something else, the window will warn you by displaying the function it is tied to below the current keys box, once the name and trigger are chosen just click the close button

7. After closing the Customize keyboard window the macro settings will save and it should be ready to record the instructions for the macro, an audiotape (nice)will appear next to the mouse cursor indicating that it is recording, proceed to ONLY HIT THE KEYBOARD SEQUENCE FOR THE SYMBOL, and then on the code group hit stop recording (has a blue square to the left, it should be where the record macro button was)

I found this but I am unsure if it will be of any help as I have never used MAC:

https://www.geoff-hart.com/resources/accents-mac.pdf

Found on the webt the one on your post: U+2234

And the complementary: U+2235

The combination of keys for the Therefore symbol (∴) is Alt + 8756 on:

• Microsoft Word 2016

• Windows 10 x64

• Installed languages

  • Spanish (Latinoamerican)

  • English (United States)

• Current OS language: Spanish

• Current Microsoft Office Language: Spanish

If after the audiotape appeaerd next to the mouse cursor you clicked anything else or hit any button not related to the function you wanted it to do I would recommend to stop the macro recording, delete it and astart over again, I am quite unsure if it would cause any issues but I would not want to risk my work on a gamble.

To test it just click anywhere on the document and hit the key or combination of keys chosen to trigger the macro.

If you need to delete the macro just go to the developer tab on the ribbon menu and on the code group click the macros button, a window will pop-up and on the search bar write down the name of the macro (the one without spaces, not the description) or scroll down the list (if you chose to follow my suggestion and added the Symbol part tot he name you will find all the symbols next to each other as the list is arranged alphabetically), click once of the macro of interest to select it and hit the delete button, just be aware that this cannot be undone and if you want the macro back you will have to create a new one.

Edit 01:

-Fixed some formatting errors

-Added a line regarding a combination of keys for a symbol

-Added information regarding the combination of keys for the therefore symbol on MAC

As stated in the comments, you get the symbols in mathmode simply by writing them down. Packages like amsmath and amssymb support you.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\newtheorem{theorem}{THEOREM}
\newtheorem{proof}{PROOF}
\begin{document}
\begin{theorem}
If an operator has both Left Identity and
Right Identity then it is \emph{UNIQUE}.
\end{theorem}
\begin{proof}
Let $e_{l}$ is left identity 
$\therefore e_{l} * e_{r} \implies e_{r}$
\end{proof}
\end{document}