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?
Logical equivalence and equality
equality
Equality is a syntactic notion, equivalence is a semantic notion. Two expressions are equal if they are the same expression — in other words, an expression is only equal to itself. Two logical expressions are equivalent if they have the same truth value in every interpretation.Two equal expressions are always equivalent, but the converse doesn't hold. For example, $A \equiv \lnot\lnot A$ but $A \neq \lnot\lnot A$.