From ProofWiki
Jump to navigation Jump to search


Contradictory Propositional Formulas

Let $\Delta$ be a set of propositional formulas.

Then $\Delta$ is contradictory if and only if there exists some propositional formula $P$ such that $P \in \Delta$ and $\neg P \in \Delta$.

Contradictory Branch

Let $T$ be a labeled tree for propositional logic.

Let $\Gamma$ be a branch of $T$.

Then $\Gamma$ is a contradictory branch if and only if, for some WFF of propositional logic $\mathbf A$, both $\mathbf A$ and $\neg \mathbf A$ occur along $\Gamma$.

Contradictory Statements

Two statements $p$ and $q$ are said to be contradictory if and only if:

whenever $p$ is true, $q$ is false.


whenever $q$ is true, $p$ is false.

Also see