Post History
#2: Post edited
Indisputably, X⊕ ¬X ≡ X ∨ ¬X.But without doing all the algebra and operations at the link below, how can I determine or see - by inspection - whether an Exclusive Or (⊕) can be simplified to an Inclusive Or? To wit, when does ⊕ imply Inclusive Or?- >[Now this is odd, yet an insightful lesson. I began this by saying that "Either... or..." is an exclusive-or; and yet, we simplified the proposition to the exact same one, but using an inclusive-or. Upon reflection, this makes perfect sense: we can use an inclusive-or, because we can't have A and ¬ A both be true. So we could still use the inclusive-or but have the whole proposition still function like an exclusive-or.](https://philosophy.stackexchange.com/a/134719)
- I am dodging algebra, as I am assuming that the poster (his name is [poop man](https://philosophy.stackexchange.com/users/111311/poop-man) in the quote above) intuited that he can simplify the ⊕ in
- >(A ∧ ¬ B) ⊕ (¬ A ∧ C)
- to an inclusive Or.
- To wit, poop man started from intuition, then worked on the algebra. I'm assuming that he didn't dive head first into all that algebra, without any inkling or intuition whether he can simplify ⊕ into an inclusive-or.
- Is X⊕ ¬X ≡ X ∨ ¬X ?
- Anyways, without doing all the algebra and operations at the link below, how can I determine or see - by inspection - whether an Exclusive Or (⊕) can be simplified to an Inclusive Or? To wit, when does ⊕ imply Inclusive Or?
- >[Now this is odd, yet an insightful lesson. I began this by saying that "Either... or..." is an exclusive-or; and yet, we simplified the proposition to the exact same one, but using an inclusive-or. Upon reflection, this makes perfect sense: we can use an inclusive-or, because we can't have A and ¬ A both be true. So we could still use the inclusive-or but have the whole proposition still function like an exclusive-or.](https://philosophy.stackexchange.com/a/134719)
- I am dodging algebra, as I am assuming that the poster (his name is [poop man](https://philosophy.stackexchange.com/users/111311/poop-man) in the quote above) intuited that he can simplify the ⊕ in
- >(A ∧ ¬ B) ⊕ (¬ A ∧ C)
- to an inclusive Or.
- To wit, poop man started from intuition, then worked on the algebra. I'm assuming that he didn't dive head first into all that algebra, without any inkling or intuition whether he can simplify ⊕ into an inclusive-or.
#1: Initial revision
When does Exclusive Or, ⊕, automatically become Inclusive Or?
Indisputably, X⊕ ¬X ≡ X ∨ ¬X. But without doing all the algebra and operations at the link below, how can I determine or see - by inspection - whether an Exclusive Or (⊕) can be simplified to an Inclusive Or? To wit, when does ⊕ imply Inclusive Or? >[Now this is odd, yet an insightful lesson. I began this by saying that "Either... or..." is an exclusive-or; and yet, we simplified the proposition to the exact same one, but using an inclusive-or. Upon reflection, this makes perfect sense: we can use an inclusive-or, because we can't have A and ¬ A both be true. So we could still use the inclusive-or but have the whole proposition still function like an exclusive-or.](https://philosophy.stackexchange.com/a/134719) I am dodging algebra, as I am assuming that the poster (his name is [poop man](https://philosophy.stackexchange.com/users/111311/poop-man) in the quote above) intuited that he can simplify the ⊕ in >(A ∧ ¬ B) ⊕ (¬ A ∧ C) to an inclusive Or. To wit, poop man started from intuition, then worked on the algebra. I'm assuming that he didn't dive head first into all that algebra, without any inkling or intuition whether he can simplify ⊕ into an inclusive-or.