# Logical equivalence and equality

Let be $F=(A\land B)$ and $G=\neg(\neg A \lor \neg B)$. Which of the following statements are correct

$F=G, F\equiv G, \neg F=\neg G, \neg F\equiv\neg G$?

Is there a difference?

• Hello! We discourage posts that simply state a problem out of context, and expect the community to solve it. What are your thoughts? What have you tried? Where did you get stuck? Did you try writing out a truth table? Assuming you tried to solve it yourself and got stuck, it may be helpful if you wrote your thoughts and what you could not figure out.
– D.W.
Commented Oct 26, 2015 at 0:32

Two equal expressions are always equivalent, but the converse doesn't hold. For example, $A \equiv \lnot\lnot A$ but $A \neq \lnot\lnot A$.
• Thank you for firstly for your answer! So, the right statements would be $\neg F\equiv \neg G$ and $F\equiv G$. I've proved these with a truth table. Commented Oct 25, 2015 at 11:37
• The symbols $\leftrightarrow$ and $\Leftrightarrow$ don't have any standard interpretation. You'll have to explain what these mean to you. Commented Apr 30, 2020 at 15:48