diff --git a/Logic/General_concepts/Logical_consistency.md b/Logic/General_concepts/Logical_consistency.md index 549383a..9bf3790 100644 --- a/Logic/General_concepts/Logical_consistency.md +++ b/Logic/General_concepts/Logical_consistency.md @@ -42,20 +42,12 @@ $$ $ \{P, Q\} $ form a consistent set because there is at least one assignment when both propositions are true. In fact there are two (corresponding to each disjunct) but one is sufficient. -``` -P Q P ∨ Q Q -T T T T * -T F T F -F T T T * -F F F F -``` - | $P$ | $Q$ | $ P \lor Q $ | $Q$ | | --- | --- | ------------ | --- | -| 0 | 0 | 0 | 0 | -| 0 | 1 | 1 | 1 | -| 1 | 0 | 1 | 1 | -| 1 | 1 | 1 | 1 | +| T | T | T | T | +| T | F | T | F | +| F | T | T | T | +| F | F | F | F | ## Derivation diff --git a/Logic/General_concepts/Logical_equivalence.md b/Logic/General_concepts/Logical_equivalence.md index bac9dae..d604f27 100644 --- a/Logic/General_concepts/Logical_equivalence.md +++ b/Logic/General_concepts/Logical_equivalence.md @@ -22,28 +22,19 @@ $$ ### Truth-tables -``` -P Q P ⊃ Q -T T T -T F F -F T T -F F T -``` - -``` -P Q ~ P ∨ Q -T T T -T F F -F T T -F F T -``` +| $P$ | $Q$ | $ P \supset Q $ | $ \sim P \lor Q$ | +| --- | --- | --------------- | ---------------- | +| T | T | T | T | +| T | F | T | F | +| F | T | T | T | +| F | F | F | T | ### Derivation > Propositions $P$ and $Q$ are equivalent in a system of [derivation](Formal%20proofs%20in%20propositional%20logic.md) for propositional logic if $Q$ is derivable from $P$ and $P$ is derivable from $Q$. -Note that the property of equivalence stated in terms of derivablity above is identical to the derivation rule for the [material biconditional](Biconditional%20Introduction.md): +Note that the property of equivalence stated in terms of derivablity above is identical to the derivation rule for the [material biconditional](/Logic/Proofs/Biconditional_Introduction.md): -![bi-intro.png](../img/bi-intro.png) +![bi-intro.png](/img/bi-intro.png) //TODO: Add demonstration of this by deriving two equivalents from one of DeMorgan's Laws diff --git a/Logic/General_concepts/Logical_indeterminacy.md b/Logic/General_concepts/Logical_indeterminacy.md index a9b75c3..d2cd4b6 100644 --- a/Logic/General_concepts/Logical_indeterminacy.md +++ b/Logic/General_concepts/Logical_indeterminacy.md @@ -44,8 +44,7 @@ P ### Truth-table -``` -P P -T T -F F -``` +| $P$ | $P$ | +| --- | --- | +| T | T | +| F | F |