In propositional logic we have the DeMorgan's laws:
$$\lnot (p\lor q) \Leftrightarrow \lnot p\land \lnot q$$ $$\lnot (p\land q) \Leftrightarrow \lnot p\lor \lnot q$$
I would like to teach the laws of logic to my students, but changing the symbol $\Leftrightarrow$, because I don't want to confuse them with $\leftrightarrow$. Can I introduce =, instead of $\Leftrightarrow$? what is the default symbol of the logic equivalence used to researchers in this area?
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3 Answers
Typically I have seen $\equiv $ used for logical equivalence.
You can use a triple bar symbol or a quadruple bar symbol.
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As someone has mentioned, you use this symbol $\equiv$, which is simply "\equiv".
If you assign them any type of homework dealing with logical equivalences and solving them, then they can use Microsoft Word. Just go to Insert > Equation. There should be an Equation tab open up on the top with the other tabs.
As pictured, there is almost every symbol we use in equivalences/equations. When you're writing in the equation field on the word document, you can write out the shortcut that appears when you float the mouse over a symbol.
Interesting enough, the same shortcuts you use in Word to write the symbol are also the same used here. For example, you write \vee to make $\vee$, just like in Microsoft Office too.
Here's an example of what I could do with Microsoft Word.