# How to represent a logic equivalence?

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?

Thanks

• This depends on how much detail you want to give. Both $\iff$ and $\leftrightarrow$ have their own (different) meaning, but due to completeness not really.Whatever you do $=$ is simply wrong. Oct 3 '15 at 18:55

Typically I have seen $\equiv$ used for logical equivalence.

• What about the logical implication ($\Rightarrow$)? thank you for your answer Oct 5 '15 at 3:21
• But the Unicode character ≡, U+2261, has the name “identical to”. On the other hand, the quadruple bar one, ≣, U+2263, has the name “strictly equivalent to”, although I don’t what to think about the “strictly” in the name, especially that there seems to not be any “equivalent to” for short. It seems the quadruple bar is less ambiguous. Also, someone said elsewhere, the triple bar often means something else with maths: congruence. Apr 30 '20 at 16:08

You can use a triple bar symbol or a quadruple bar symbol.

• What about the logical implication (⇒)? thank you for your answer Oct 6 '15 at 4:44
• @user42912 Personally speaking I prefer not to use any of those symbols. I prefer to use 'C' for logical implication, and 'E' for logical equivalence. What you meant to write in your post I would write as ENApqKNpNq, ENKpqANpNq or E(N(A(p, q)), K(N(p), N(q))) and E(N(K(p, q)), A(N(p), N(q))). A significant amount of research into propositional calculi in the 20th century got conducted in Polish notation. There's still some research in that area using either Polish notation or prefix notation. Oct 6 '15 at 12:30

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.

• What about the logical implication (⇒)? thank you for your answer Oct 6 '15 at 4:44
• I would go with the three lines symbol. This is the only used we prefer to use for our discrete math more than the one you showed. Oct 6 '15 at 21:26