A contradiction is a formula that is always false regardless of the truth assignment. A contradiction is also called a unsatsifiable or an inconsistent formula.
Consider the propositional formula A ∧ ¬A.
The truth table below shows this to be always false regardless of the truth value of A.
A | ¬A | A ∧ ¬A |
|---|---|---|
t | f | f |
f | t | f |
Doets, Kees. From Logic to Logic Programming. MIT Press, 1994.
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