Definition:Contradictory
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Definition
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:
and: