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16
Logic/General_concepts/Logical_consistency.md
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@ -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\} $ 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 $ | $Q$ | | $P$ | $Q$ | $ P \lor Q $ | $Q$ |
| --- | --- | ------------ | --- | | --- | --- | ------------ | --- |
| 0 | 0 | 0 | 0 | | T | T | T | T |
| 0 | 1 | 1 | 1 | | T | F | T | F |
| 1 | 0 | 1 | 1 | | F | T | T | T |
| 1 | 1 | 1 | 1 | | F | F | F | F |
## Derivation ## Derivation

25
Logic/General_concepts/Logical_equivalence.md
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@ -22,28 +22,19 @@ $$
### Truth-tables ### Truth-tables
``` | $P$ | $Q$ | $ P \supset Q $ | $ \sim P \lor Q$ |
P Q P ⊃ Q | --- | --- | --------------- | ---------------- |
T T T | T | T | T | T |
T F F | T | F | T | F |
F T T | F | T | T | T |
F F T | F | F | F | T |
```
```
P Q ~ P ∨ Q
T T T
T F F
F T T
F F T
```
### Derivation ### 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 $Q$. > 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 //TODO: Add demonstration of this by deriving two equivalents from one of DeMorgan's Laws

9
Logic/General_concepts/Logical_indeterminacy.md
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@ -44,8 +44,7 @@ P
### Truth-table ### Truth-table
``` | $P$ | $P$ |
P P | --- | --- |
T T | T | T |
F F | F | F |
```