# Logical Proofs

This page is a learning resource for those people who want to learn how to do logical proofs. Disclaimer: The information provided here is solely from my own experience in a university logic class.

## Propositional Translation

For the first part, we are going to learn how to translate natural language into logical expressions. For this we'll use the following tables:

Symbol Meaning Translations
${\displaystyle \lnot A}$

${\displaystyle \sim A\,}$

Negation Not A
${\displaystyle (A\vee B)}$ Or A or B
${\displaystyle (A\land B)}$

${\displaystyle (A\cdot B)}$

And A and B
${\displaystyle (A\rightarrow B)}$

${\displaystyle (A\Rightarrow B)}$
${\displaystyle (A\supset B)}$

Implication If A then B
A implies B
${\displaystyle (A\leftrightarrow B)}$

${\displaystyle (A\Leftrightarrow B)}$
${\displaystyle (A\equiv B)}$

Equivalence A if and only if B