Double Negation with Erroneous Conjunction

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Source Work

1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.):

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.


Sources