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
- 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.2$: Truth functions and truth tables: Example $1.6 \ \text{(c)}$