equivalent Equivalent3 2002-12-17 11:34:21 2007-05-16 17:25:16 Definition logically equivalent equivalent equivalence formal logic % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Two statements $A$ and $B$ are said to be \emph{logically equivalent} (typically shortened to \emph{equivalent}) when $A$ is true if and only if $B$ is true (that is, $A$ implies $B$ and $B$ implies $A$). This is usually written as $A \Leftrightarrow B$. For example, for any integer $z$, the statement ``$z$ is positive'' is equivalent to ``$z$ is not negative and $z\neq 0$''.