🚀 go-pugleaf

In article <1992Oct15.224329.20578@agt.uucp> Brian F G Bidulock <bbidulo1%agt@cs.ualberta.ca> writes:
>In article <rkaivola.718902434@mits> Risto Kaivola,
>rkaivola@mits.mdata.fi writes:
>>"Tom will visit us only if we invite him.",
>>is the correct formalization
>>
>>A = "Tom will visit us."
>>
>>B = "We invite him."
>>
>>A  -->  B
>
>How about:
>~A --> ~B
>or
>"If we don't invite Tom, he will not visit us."  == "Tom will visit us
>only if we invite him."

Half right.  What you symbolized by ~A -> ~B would be translated as,
"If Tom does not visit us, we did not invite him."  This would be false
only if ( I just love this construction!) Tom didn't visit us, and we did
invite him, and true otherwise.  This means that the case in which Tom
visits us even though we did NOT invite him is true for ~A -> ~B, but is
the sole false assignment of truth values for A -> B.  In other words, 
they aren't logically equivalent propositions.

Your English translation of ~A -> ~B is incorrect as a translation, 
but it IS logically equivalent to the original statement.  It's actually 
of the form ~B -> ~A (which is very likely what you meant to write in the
first place), and has exactly the same truth conditions as A -> B.

--Dan