# Double Negation with Erroneous Conjunction

## Source Work

Chapter $1$: Informal statement calculus
$1.2$. Truth functions and truth tables: Example $1.6 \ \text{(c)}$

## Mistake

$\paren {p \leftrightarrow \paren {\land \paren {\sim p} } }$ is a tautology.

## Correction

As it stands, this statement is meaningless, as $\land$ is a binary operator.

The most obvious assumption is that $\land$ is a typo for $\sim$, and that:

$\paren {p \leftrightarrow \paren {\sim \paren {\sim p} } }$ is a tautology.

is meant.

See Double Negation/Formulation 2 for an analysis of this.

Note that in Alan G. Hamilton: Logic for Mathematicians (2nd ed.):

$\sim$ is the symbol used for $\neg$, the logical negation operator
$\leftrightarrow$ is the symbol used for $\iff$, the biconditional operator.