(related to Lemma: It is true that something can be (either) true or false)
We want to show that for every proposition \(x\) the disjunction \(x\vee \neg x\) is a tautology. This can be easily verified: By definition of disjunction, any possible semantics of \(x\) makes the compound proposition \(x\vee \neg x\) valid:
\([[x]]_I\) | \([[x]]_I\) | \([[x\vee \neg x]]_I\) |
---|---|---|
\(1\) | \(0\) | \(1\) |
\(0\) | \(1\) | \(1\) ∎ |