(related to Lemma: Mixing-up the Inclusive and Exclusive Disjunction)
We want to prove that the mixing-up the inclusive and exclusive disjunction is a fallacy. * The fallacy can be formulated in propositional logic as $(p\vee q)\wedge p\Rightarrow \neg q.$ * We get the following truth table of the function due to the definition of negation and implication:
| $[[p]]_I$ | $[[q]]_I$ | $[[p\vee q]]_I$ | $[[ \neg q]]_I$ |
|---|---|---|---|
| $0$ | $0$ | $0$ | $1$ |
| $0$ | $1$ | $1$ | $0$ |
| $1$ | $0$ | $1$ | $1$ |
| $1$ | $1$ | $1$ | $0$ |
