2022-04-23 13:26:53 +01:00
|
|
|
---
|
2024-06-16 18:15:03 +01:00
|
|
|
tags:
|
|
|
|
|
- propositional-logic
|
|
|
|
|
- logic
|
2022-04-23 13:26:53 +01:00
|
|
|
---
|
|
|
|
|
|
2022-12-25 15:00:05 +00:00
|
|
|
# Disjunction Elimination
|
|
|
|
|
|
2024-02-02 15:58:13 +00:00
|
|
|
This rule is sometimes also referred to as _Constructive Dilemma_. This can be a
|
|
|
|
|
bit tricky to understand because the goal is to derive or _introduce_ a new
|
|
|
|
|
proposition separate from the disjunction you start out with. This may be
|
|
|
|
|
disjunction, a single proposition or a proposition containing any other logical
|
|
|
|
|
connective. You do this by constructing two sub-proofs, one for each of the
|
|
|
|
|
disjuncts comprising the disjunction you start out with. If you can derive your
|
|
|
|
|
target proposition as the conclusion of each subproof then you may invoke the
|
|
|
|
|
conclusion in the main proof and take it to be derived.
|
2022-04-23 13:26:53 +01:00
|
|
|
|
2024-02-16 16:14:01 +00:00
|
|
|
|
2022-04-23 13:26:53 +01:00
|
|
|
|
2024-02-02 15:58:13 +00:00
|
|
|
_Here is an example where Disjunction Elimination is used to derive a new
|
|
|
|
|
disjunction._
|
2022-04-23 13:26:53 +01:00
|
|
|
|
2024-02-16 16:14:01 +00:00
|
|
|
|
2022-04-23 13:26:53 +01:00
|
|
|
|
2024-02-02 15:58:13 +00:00
|
|
|
_Here are two further examples that use Disjunction Elimination to derive
|
|
|
|
|
singular propositions_
|
2022-04-23 13:26:53 +01:00
|
|
|
|
2024-02-16 16:14:01 +00:00
|
|
|
 
|
