Cheap and Secure Web Hosting Provider : See Now

# [Solved]: Logical equivalence and equality

, ,
Problem Detail:

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?

#### Answered By : Yuval Filmus

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 $A \neq \lnot\lnot A$.

###### Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/48698

3.2K people like this