🚀 go-pugleaf

>>A-->B = if A then B
>>A<-->B = A if and only if B
>>A<--B = A only if B = if B then A  This is read: A is true only if B is
>>true since a true statement cannot imply a falsehood.

>  Appologies, this is clearly wrong. :(  That's what I get for posting
>late at night and thinking about things like necessary and sufficient.
>Guess that puts me one up on Dogwood (Much Ado About Nothing) as he only
>wanted to be written down an ass.  :):):)
>  Let's try again:  How about A only if B = (B-->A)&(-B-->-a)

  Nope, this is just if and only if

>bv

  Okay, let's go for the hat trick here.
1.  Tim will come to dinner if we invite him
2.  Tim will come to dinner if and only if we invite him
3.  Tim will come to dinner only if we invite him.

A = Tim will come to dinner; B = We invite him
so we have
1.  B-->A that is, tim will come if invited
2.  B<-->A  tim will come if invited, and if tim comes he was invited
3'.  B<--A  if tim comes he was invited
  Claim is that 3' = 3
  Tim will come only if we invite him means that if tim comes he was
invited.  Or, contrapositive, if he is not invited, he will not come:
i.e., -B-->-A  But this is equivalent to --a-->--B; i.e., A-->B
  The Phoenix rises
confusion of logical and causal thinking.

bv