Either or and At least one

[Dancingbambarina]

Surely the idea of at least one happening is the same as both not occuring.

Not A --> B
Not B --> A

A --> NotB
B --> NotA



With both statements (made respectively), one occurs and the doesn't, so how does this differ actually?

[Dave Killoran]

The idea of "at least one happening" means you can't have both not occur. That is the same as:

Not A --> B
Not B --> A

However, under that scenario, why can't both a and B occur? No sufficient condition stops them from both occurring in that scenario because those statements only are in force when one doesn't happen.

However, when we look at:

A --> NotB
B --> NotA

These two explicitly stop both from occurring, so they are very different than the first set. But, under the second set of statements, you could have neither.

Do some poking around on this forum for posts on "either/or" and either/or but not both." There's lots of discussion of how either/or agree with your first set of statements, and then how adding "but not both" then draws in the second statement." This was far more important back in the days of Logic Games, but it's still good to know now

Thanks!

[Dancingbambarina]

Surely the idea of at least one happening is the same as both not occuring.

Not A --> B
Not B --> A

A --> NotB
B --> NotA



With both statements (made respectively), one occurs and the doesn't, so how does this differ actually?

Thanks so much Dave!!!!!1