Talk:Converse (logic)
Latest comment: 19 years ago by Gene.arboit in topic Converse or inverse
Converse or inverse
This article should be merged with Inverse (logic)? Gene.arboit 02:18, 11 September 2005 (UTC)
- I don't think the two articles should be merged. The converse is a much more imoprtant and complex idea in mathematics than the logical inverse is. For example, consider the following proposition:
- A → (B → C)
- A naïve understanding of the converse says that the converse of this is:
- (B → C) → A
- But in fact, as mathematicains and logicians understand and use the word "converse", the original proposition is understood to be equivalent to :
- (A ∧ B) → C
- and so its converse is:
- C → (A ∧ B).
- and in general, one wants equivalent statements to have equivalent converses, which is not true of the simple definition of the converse of (A→B) as being (B→A). -- Dominus 04:06, 12 September 2005 (UTC)
- I think I see the point. (B → C) → A, i.e. (B ∧ ¬ C) ∨ A, is not equivalent to C → (A ∧ B), i.e. ¬ C ∨ (A ∧ B). Should this be mentioned in the converse article, perhaps? Gene.arboit 02:57, 14 September 2005 (UTC)